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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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Published in: | Discrete Applied Mathematics 2019-06, Vol.263, p.51-58 |
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Main Authors: | , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0166-218X 1872-6771 |
DOI: | 10.1016/j.dam.2018.03.043 |