Volume 50, Number 2, April-June 2016
Special issue: Research on Optimization and Graph Theory dedicated to COSI 2013
|Page(s)||233 - 239|
|Published online||21 March 2016|
Generalization of the total outer-connected domination in graphs
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.
Accepted: 1 June 2015
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 k ≥ 1 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 γktc(G) , is the minimum cardinality of a total outer-k-connected component dominating set of G. We obtain several general results and bounds for γktc(G), and we determine exact values of γktc(G) for some special classes of graphs G.
Mathematics Subject Classification: 05C69
Key words: Total domination / total outer-connected domination
© EDP Sciences, ROADEF, SMAI 2016
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