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Abstract
The neighbourhood of a vertexvof a graphGis the setN(v) of all verticesadjacent tovinG. ForD⊆V(G) we defineD=V(G)\D. A setD⊆V(G) is called a super dominating set if for every vertexu∈D, there existsv∈Dsuch thatN(v)∩D={u}. The super domination number ofGis theminimum cardinality among all super dominating sets inG. In this article weobtain closed formulas and tight bounds for the super dominating number oflexicographic product graphs in terms of invariants of the factor graphs involvedin the product. As a consequence of the study, we show that theproblem offinding the super domination number of a graph is NP-Hard (16) (PDF) On the super domination number of lexicographic product graphs. Available from: https://www.researchgate.net/publication/315382754_On_the_super_domination_number_of_lexicographic_product_graphs [accessed Jul 28 2020].
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Authors (4)
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Juan A. RODRíGUEZ-VELáZQUEZ
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Rita Zuazua
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- Category:
- Articles
- Type:
- artykuły w czasopismach
- Published in:
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DISCRETE APPLIED MATHEMATICS
no. 263,
pages 118 - 129,
ISSN: 0166-218X - Language:
- English
- Publication year:
- 2019
- Bibliographic description:
- Dettlaff M., Lemańska M., Rodríguez-Velázquez J., Zuazua R.: On the super domination number of lexicographic product graphs// DISCRETE APPLIED MATHEMATICS -Vol. 263, (2019), s.118-129
- DOI:
- Digital Object Identifier (open in new tab) 10.1016/j.dam.2018.03.082
- Verified by:
- Gdańsk University of Technology
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