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Total k-domination in strong product graphs

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 the s...

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Bibliographic Details
Published in:Discrete Applied Mathematics 2019-06, Vol.263, p.51-58
Main Authors: Bermudo, S., Hernández-Gómez, J.C., Sigarreta, J.M.
Format: Article
Language:English
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Summary: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 the strong product of two graphs. In particular, we investigate the relationship between the total k-domination number of the strong product of two graphs with the domination, k-domination and total k-domination numbers of the factors in the product.
ISSN:0166-218X
1872-6771
DOI:10.1016/j.dam.2018.03.043