1. ON THE TOTAL k-DOMINATION IN GRAPHS.
- Author
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BERMUDO, SERGIO, HERNÁNDEZ-GÓMEZ, JUAN C., and SIGARRETA, JOSÉ M.
- Subjects
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GEOMETRIC vertices , *GRAPH theory , *DOMINATING set , *ANALYTIC geometry , *GRAPH connectivity - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2018
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