Geodesic
Characterization of trees with equal 2-domination number and domination number plus two
Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 4, pp. 687-697 Cet article a éte moissonné depuis la source Library of Science

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Let G = (V(G),E(G)) be a simple graph, and let k be a positive integer. A subset D of V(G) is a k-dominating set if every vertex of V(G) - D is dominated at least k times by D. The k-domination number γₖ(G) is the minimum cardinality of a k-dominating set of G. In [5] Volkmann showed that for every nontrivial tree T, γ₂(T) ≥ γ₁(T)+1 and characterized extremal trees attaining this bound. In this paper we characterize all trees T with γ₂(T) = γ₁(T)+2.
Keywords: 2-domination number, domination number, trees 
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Chellali, Mustapha; Volkmann, Lutz. Characterization of trees with equal 2-domination number and domination number plus two. Discussiones Mathematicae. Graph Theory, Tome 31 (2011) no. 4, pp. 687-697. http://geodesic.mathdoc.fr/item/DMGT_2011_31_4_a4/

[1] M. Chellali, T.W. Haynes and L. Volkmann, Global offensive alliance numbers in graphs with emphasis on trees, Australasian J. Combin. 45 (2009) 87-96.

[2] J.F. Fink and M.S. Jacobson, n-domination in graphs, in: Y. Alavi and A.J. Schwenk, editors, ed(s), Graph Theory with Applications to Algorithms and Computer Science (Wiley, New York, 1985) 283-300.

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

[4] S.M. Hedetniemi, S.T. Hedetniemi, and P. Kristiansen, Alliances in graphs, J. Combin. Math. Combin. Comput. 48 (2004) 157-177.

[5] L. Volkmann, Some remarks on lower bounds on the p-domination number in trees, J. Combin. Math. Combin. Comput. 61 (2007) 159-167.