Geodesic
Hereditary domination and independence parameters
Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 239-248

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For a graphical property P and a graph G, we say that a subset S of the vertices of G is a P-set if the subgraph induced by S has the property P. Then the P-domination number of G is the minimum cardinality of a dominating P-set and the P-independence number the maximum cardinality of a P-set. We show that several properties of domination, independent domination and acyclic domination hold for arbitrary properties P that are closed under disjoint unions and subgraphs.
Keywords: domination, hereditary property, independence 
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Goddard, Wayne; Haynes, Teresa; Knisley, Debra. Hereditary domination and independence parameters. Discussiones Mathematicae. Graph Theory, Tome 24 (2004) no. 2, pp. 239-248. http://geodesic.mathdoc.fr/item/DMGT_2004_24_2_a6/