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On the Total k-Domination in Graphs
- Source :
- Discussiones Mathematicae Graph Theory, Vol 38, Iss 1, Pp 301-317 (2018)
- Publication Year :
- 2018
- Publisher :
- University of Zielona Góra, 2018.
-
Abstract
- 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.
Details
- Language :
- English
- ISSN :
- 20835892
- Volume :
- 38
- Issue :
- 1
- Database :
- Directory of Open Access Journals
- Journal :
- Discussiones Mathematicae Graph Theory
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.801c3de9ab044f24bb02bdd415cbe58e
- Document Type :
- article
- Full Text :
- https://doi.org/10.7151/dmgt.2016