Geodesic
Graphs with large double domination numbers
Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 13-28

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In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V(G) is a double dominating set of G if S dominates every vertex of G at least twice. The minimum cardinality of a double dominating set of G is the double domination number γ_×2(G). If G ≠ C₅ is a connected graph of order n with minimum degree at least 2, then we show that γ_×2(G) ≤ 3n/4 and we characterize those graphs achieving equality.
Keywords: bounds, domination, double domination, minimum degree two 
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Henning, Michael. Graphs with large double domination numbers. Discussiones Mathematicae. Graph Theory, Tome 25 (2005) no. 1-2, pp. 13-28. http://geodesic.mathdoc.fr/item/DMGT_2005_25_1-2_a1/