Geodesic
Full domination in graphs
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 43-62
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For each vertex v in a graph G, let there be associated a subgraph H_v of G. The vertex v is said to dominate H_v as well as dominate each vertex and edge of H_v. A set S of vertices of G is called a full dominating set if every vertex of G is dominated by some vertex of S, as is every edge of G. The minimum cardinality of a full dominating set of G is its full domination number γ_FH(G). A full dominating set of G of cardinality γ_FH(G) is called a γ_FH-set of G. We study three types of full domination in graphs: full star domination, where H_v is the maximum star centered at v, full closed domination, where H_v is the subgraph induced by the closed neighborhood of v, and full open domination, where H_v is the subgraph induced by the open neighborhood of v.
Keywords: full domination, full star domination, full closed domination, full open domination 
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Brigham, Robert; Chartrand, Gary; Dutton, Ronald; Zhang, Ping. Full domination in graphs. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 43-62. http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a3/

[1] T. Gallai, Über extreme Punkt- und Kantenmengen, Ann. Univ. Sci. Budapest, Eötvös Sect. Math. 2 (1959) 133-138.

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

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

[4] S.R. Jayaram, Y.H.H. Kwong and H.J. Straight, Neighborhood sets in graphs, Indian J. Pure Appl. Math. 22 (1991) 259-268.

[5] E. Sampathkumar and P.S. Neeralagi, The neighborhood number of a graph, Indian J. Pure Appl. Math. 16 (1985) 126-136.

[6] O. Ore, Theory of Graphs, Amer. Math. Soc. Colloq. Publ. 38 (Amer. Math. Soc. Providence, RI, 1962).