1. On the Total k-Domination in Graphs
- Author
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Bermudo Sergio, Hernández-Gómez Juan C., and Sigarreta José M.
- Subjects
k-domination ,total k-domination ,k-tuple domination ,k-tuple total domination ,05c69 ,Mathematics ,QA1-939 - 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.
- Published
- 2018
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