Let be a graph without an isolated vertex. A set is a total dominating set if is a dominating set, and the induced subgraph does not contain an isolated vertex. The total domination number of is the minimum cardinality of a total dominating set of . A set is a total outer-connected dominating set if is a total dominating set, and the induced subgraph is connected. The total outer-connected domination number of is the minimum cardinality of a total outer-connected dominating set of . In this paper we generalize the total outer-connected domination number in graphs. Let be an integer. A set is a total outer--connected component dominating set if is a total dominating and the induced subgraph has exactly connected component(s). The total outer--connected component domination number of , denoted by , is the minimum cardinality of a total outer--connected component dominating set of . We obtain several general results and bounds for , and we determine exact values of for some special classes of graphs .
Mots-clés : Total domination, total outer-connected domination
@article{RO_2016__50_2_233_0, author = {Rad, Nader Jafari and Volkmann, Lutz}, title = {Generalization of the total outer-connected domination in graphs}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {233--239}, publisher = {EDP-Sciences}, volume = {50}, number = {2}, year = {2016}, doi = {10.1051/ro/2015016}, mrnumber = {3479866}, zbl = {1335.05134}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2015016/} }
TY - JOUR AU - Rad, Nader Jafari AU - Volkmann, Lutz TI - Generalization of the total outer-connected domination in graphs JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2016 SP - 233 EP - 239 VL - 50 IS - 2 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2015016/ DO - 10.1051/ro/2015016 LA - en ID - RO_2016__50_2_233_0 ER -
%0 Journal Article %A Rad, Nader Jafari %A Volkmann, Lutz %T Generalization of the total outer-connected domination in graphs %J RAIRO - Operations Research - Recherche Opérationnelle %D 2016 %P 233-239 %V 50 %N 2 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2015016/ %R 10.1051/ro/2015016 %G en %F RO_2016__50_2_233_0
Rad, Nader Jafari; Volkmann, Lutz. Generalization of the total outer-connected domination in graphs. RAIRO - Operations Research - Recherche Opérationnelle, Special issue: Research on Optimization and Graph Theory dedicated to COSI 2013 / Special issue: Recent Advances in Operations Research in Computational Biology, Bioinformatics and Medicine, Tome 50 (2016) no. 2, pp. 233-239. doi : 10.1051/ro/2015016. http://www.numdam.org/articles/10.1051/ro/2015016/
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