| Title: | Best possible upper bounds on the restrained domination number of cubic graphs |
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| Authors: | ID Brešar, Boštjan (Author)
ID Henning, Michael A. (Author) |
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| Files: |  PDF - Presentation file, download (2,13 MB)
MD5: 5A65E5661DF4CBFCFB55FA237EAE42DB
 URL - Source URL, visit https://onlinelibrary.wiley.com/doi/10.1002/jgt.23095
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| Language: | English |
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| Typology: | 1.01 - Original Scientific Article |
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| Organization: |  IMFM - Institute of Mathematics, Physics, and Mechanics
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| Abstract: | A dominating set in a graph $G$ is a set $S$ of vertices such that every vertex in $V(G) \setminus S$ is adjacent to a vertex in $S$. A restrained dominating set of $G$ is a dominating set $S$ with the additional restraint that the graph $G - S$ obtained by removing all vertices in $S$ is isolate-free. The domination number $\gamma(G)$ and the restrained domination number $\gamma_{r}(G)$ are the minimum cardinalities of a dominating set and restrained dominating set, respectively, of $G$. Let $G$ be a cubic graph of order $n$. A classical result of Reed [Combin. Probab. Comput. 5 (1996), 277-295] states that $\gamma(G) \le \frac{3}{8}n$, and this bound is best possible. To determine a best possible upper bound on the restrained domination number of $G$ is more challenging, and we prove that $\gamma_{r}(G) \le \frac{2}{5}n$. |
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| Keywords: | domination, restrained domination, cubic graphs |
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| Publication status: | Published |
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| Publication version: | Version of Record |
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| Publication date: | 01.08.2024 |
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| Year of publishing: | 2024 |
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| Number of pages: | str. 763–815 |
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| Numbering: | Vol. 106, iss. 4 |
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| PID: | 20.500.12556/DiRROS-19113  |
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| UDC: | 519.17 |
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| ISSN on article: | 0364-9024 |
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| DOI: | 10.1002/jgt.23095 |
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| COBISS.SI-ID: | 199137795 |
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| Note: |
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| Publication date in DiRROS: | 18.06.2024 |
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| Views: | 365 |
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| Downloads: | 225 |
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