1. On the Total k-Domination in Graphs
- Author
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Bermudo, Sergio, Hernández-Gómez, Juan C., and Sigarreta, José M.
- Abstract
Let G= (V, E) be a graph; a set S⊆ Vis a total k-dominating set if every vertex v∈ Vhas at least kneighbors 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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