Geodesic
Characterization of block graphs with equal 2-domination number and domination number plus one
Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 93-103

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Let G be a simple graph, and let p be a positive integer. A subset D ⊆ V(G) is a p-dominating set of the graph G, if every vertex v ∈ V(G)-D is adjacent with at least p vertices of D. The p-domination number γₚ(G) is the minimum cardinality among the p-dominating sets of G. Note that the 1-domination number γ₁(G) is the usual domination number γ(G).
Keywords: domination, 2-domination, multiple domination, block graph 
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Hansberg, Adriana; Volkmann, Lutz. Characterization of block graphs with equal 2-domination number and domination number plus one. Discussiones Mathematicae. Graph Theory, Tome 27 (2007) no. 1, pp. 93-103. http://geodesic.mathdoc.fr/item/DMGT_2007_27_1_a8/