On 3-Rainbow Domination Number of Generalized Petersen Graphs <i>P</i>(6<i>k</i>,<i>k</i>)
We obtain new results on 3-rainbow domination numbers of generalized Petersen graphs <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>(</mo><mn>6</mn><mi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/13/10/1860 |
| _version_ | 1797513098446241792 |
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| author | Rija Erveš Janez Žerovnik |
| author_facet | Rija Erveš Janez Žerovnik |
| author_sort | Rija Erveš |
| collection | DOAJ |
| description | We obtain new results on 3-rainbow domination numbers of generalized Petersen graphs <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>(</mo><mn>6</mn><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>. In some cases, for some infinite families, exact values are established; in all other cases, the lower and upper bounds with small gaps are given. We also define singleton rainbow domination, where the sets assigned have a cardinality of, at most, one, and provide analogous results for this special case of rainbow domination. |
| first_indexed | 2024-03-10T06:10:53Z |
| format | Article |
| id | doaj.art-e0e060a739554592b31832a6c83fd139 |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T06:10:53Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-e0e060a739554592b31832a6c83fd1392023-11-22T20:10:12ZengMDPI AGSymmetry2073-89942021-10-011310186010.3390/sym13101860On 3-Rainbow Domination Number of Generalized Petersen Graphs <i>P</i>(6<i>k</i>,<i>k</i>)Rija Erveš0Janez Žerovnik1FCETEA, University of Maribor, Smetanova Ulica 17, 2000 Maribor, SloveniaFME, University of Ljubljana, Aškerčeva 6, 1000 Ljubljana, SloveniaWe obtain new results on 3-rainbow domination numbers of generalized Petersen graphs <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>P</mi><mo>(</mo><mn>6</mn><mi>k</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>. In some cases, for some infinite families, exact values are established; in all other cases, the lower and upper bounds with small gaps are given. We also define singleton rainbow domination, where the sets assigned have a cardinality of, at most, one, and provide analogous results for this special case of rainbow domination.https://www.mdpi.com/2073-8994/13/10/1860rainbow dominationrainbow domination numbergeneralized Petersen graphs |
| spellingShingle | Rija Erveš Janez Žerovnik On 3-Rainbow Domination Number of Generalized Petersen Graphs <i>P</i>(6<i>k</i>,<i>k</i>) Symmetry rainbow domination rainbow domination number generalized Petersen graphs |
| title | On 3-Rainbow Domination Number of Generalized Petersen Graphs <i>P</i>(6<i>k</i>,<i>k</i>) |
| title_full | On 3-Rainbow Domination Number of Generalized Petersen Graphs <i>P</i>(6<i>k</i>,<i>k</i>) |
| title_fullStr | On 3-Rainbow Domination Number of Generalized Petersen Graphs <i>P</i>(6<i>k</i>,<i>k</i>) |
| title_full_unstemmed | On 3-Rainbow Domination Number of Generalized Petersen Graphs <i>P</i>(6<i>k</i>,<i>k</i>) |
| title_short | On 3-Rainbow Domination Number of Generalized Petersen Graphs <i>P</i>(6<i>k</i>,<i>k</i>) |
| title_sort | on 3 rainbow domination number of generalized petersen graphs i p i 6 i k i i k i |
| topic | rainbow domination rainbow domination number generalized Petersen graphs |
| url | https://www.mdpi.com/2073-8994/13/10/1860 |
| work_keys_str_mv | AT rijaerves on3rainbowdominationnumberofgeneralizedpetersengraphsipi6ikiiki AT janezzerovnik on3rainbowdominationnumberofgeneralizedpetersengraphsipi6ikiiki |