Generalization of the total outer-connected domination in graphs
RAIRO - Operations Research - Recherche Opérationnelle, Volume 50 (2016) no. 2, pp. 233-239.

Let G = ( V , E ) be a graph without an isolated vertex. A set S V is a total dominating set if S is a dominating set, and the induced subgraph G [ S ] does not contain an isolated vertex. The total domination number of G is the minimum cardinality of a total dominating set of G. A set D V is a total outer-connected dominating set if D is a total dominating set, and the induced subgraph G[V-D] is connected. The total outer-connected domination number of G is the minimum cardinality of a total outer-connected dominating set of G. In this paper we generalize the total outer-connected domination number in graphs. Let k1 be an integer. A set D V is a total outer-k-connected component dominating set if D is a total dominating and the induced subgraph G [ V - D ] has exactly k connected component(s). The total outer-k-connected component domination number of G, denoted by γ t c k ( G ) , is the minimum cardinality of a total outer-k-connected component dominating set of G. We obtain several general results and bounds for γ t c k ( G ) , and we determine exact values of γ t c k ( G ) for some special classes of graphs G.

DOI: 10.1051/ro/2015016
Classification: 05C69
Keywords: Total domination, total outer-connected domination
Rad, Nader Jafari 1; Volkmann, Lutz 2

1 Department of Mathematics, Shahrood University of Technology, P.O. Box 3619995161, Shahrood, Iran.
2 Lehrstuhl II für Mathematik, RWTH Aachen University, Templergraben 55, 52056 Aachen, Germany.
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     title = {Generalization of the total outer-connected domination in graphs},
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Rad, Nader Jafari; Volkmann, Lutz. Generalization of the total outer-connected domination in graphs. RAIRO - Operations Research - Recherche Opérationnelle, Volume 50 (2016) no. 2, pp. 233-239. doi : 10.1051/ro/2015016. http://archive.numdam.org/articles/10.1051/ro/2015016/

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