Let G = (V, E) be a graph; a set S ⊆ V is a total k-dominating set if every vertex v ∈ V has at least k neighbors in S. The total k-domination number γkt(G) is the minimum cardinality among all total k-dominating sets. In this paper we obtain several tight bounds for the total k-domination number of a graph. In particular, we investigate the relationship between the total k-domination number of a graph and the order, the size, the girth, the minimum and maximum degree, the diameter, and other domination parameters of the graph.
@article{bwmeta1.element.doi-10_7151_dmgt_2016,
author = {Sergio Bermudo and Juan C. Hern\'andez-G\'omez and Jos\'e M. Sigarreta},
title = {On the Totalk-Domination in Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {38},
year = {2018},
pages = {301-317},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_2016}
}
Sergio Bermudo; Juan C. Hernández-Gómez; José M. Sigarreta. On the Totalk-Domination in Graphs. Discussiones Mathematicae Graph Theory, Tome 38 (2018) pp. 301-317. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_2016/