Geodesic
Some remarks on α-domination
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 423-430

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Let α ∈ (0,1) and let G = (V_G,E_G) be a graph. According to Dunbar, Hoffman, Laskar and Markus [3] a set D ⊆ V_G is called an α-dominating set of G, if |N_G(u) ∩ D| ≥ αd_G(u) for all u ∈ V_G∖D. We prove a series of upper bounds on the α-domination number of a graph G defined as the minimum cardinality of an α-dominating set of G.
Keywords: α-domination, domination 
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Dahme, Franz; Rautenbach, Dieter; Volkmann, Lutz. Some remarks on α-domination. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 3, pp. 423-430. http://geodesic.mathdoc.fr/item/DMGT_2004_24_3_a5/