NP-completeness of weakly convex and convex dominating set decision problems
The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are \(NP\)-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can v...
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| Format: | Article |
| Language: | English |
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AGH Univeristy of Science and Technology Press
2004-01-01
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| Series: | Opuscula Mathematica |
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| Online Access: | http://www.opuscula.agh.edu.pl/vol24/2/art/opuscula_math_2417.pdf |
| _version_ | 1818322456231804928 |
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| author | Joanna Raczek |
| author_facet | Joanna Raczek |
| author_sort | Joanna Raczek |
| collection | DOAJ |
| description | The convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are \(NP\)-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex. |
| first_indexed | 2024-12-13T10:57:05Z |
| format | Article |
| id | doaj.art-01c0fc74494b4c4984b370f34ac02092 |
| institution | Directory Open Access Journal |
| issn | 1232-9274 |
| language | English |
| last_indexed | 2024-12-13T10:57:05Z |
| publishDate | 2004-01-01 |
| publisher | AGH Univeristy of Science and Technology Press |
| record_format | Article |
| series | Opuscula Mathematica |
| spelling | doaj.art-01c0fc74494b4c4984b370f34ac020922022-12-21T23:49:25ZengAGH Univeristy of Science and Technology PressOpuscula Mathematica1232-92742004-01-012421891962417NP-completeness of weakly convex and convex dominating set decision problemsJoanna Raczek0Gdańsk University of Technology, Department of Mathematics, ul. Narutowicza 11/12, 80-952 Gdańsk, PolandThe convex domination number and the weakly convex domination number are new domination parameters. In this paper we show that the decision problems of convex and weakly convex dominating sets are \(NP\)-complete for bipartite and split graphs. Using a modified version of Warshall algorithm we can verify in polynomial time whether a given subset of vertices of a graph is convex or weakly convex.http://www.opuscula.agh.edu.pl/vol24/2/art/opuscula_math_2417.pdfdominating set\(NP\)-completenessdistanceconvex set |
| spellingShingle | Joanna Raczek NP-completeness of weakly convex and convex dominating set decision problems Opuscula Mathematica dominating set \(NP\)-completeness distance convex set |
| title | NP-completeness of weakly convex and convex dominating set decision problems |
| title_full | NP-completeness of weakly convex and convex dominating set decision problems |
| title_fullStr | NP-completeness of weakly convex and convex dominating set decision problems |
| title_full_unstemmed | NP-completeness of weakly convex and convex dominating set decision problems |
| title_short | NP-completeness of weakly convex and convex dominating set decision problems |
| title_sort | np completeness of weakly convex and convex dominating set decision problems |
| topic | dominating set \(NP\)-completeness distance convex set |
| url | http://www.opuscula.agh.edu.pl/vol24/2/art/opuscula_math_2417.pdf |
| work_keys_str_mv | AT joannaraczek npcompletenessofweaklyconvexandconvexdominatingsetdecisionproblems |