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Full domination in graphs

100%

Brigham R., Chartrand G., Dutton R., Zhang P.

Discussiones Mathematicae Graph Theory

2001

tom 21

nr 1

43-62

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.

Ograniczanie wyników

1 Discussiones Mathematicae Graph Theory

1 Brigham R.

1 Chartrand G.

1 Dutton R.

1 Zhang P.

1 2001

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Full domination in graphs