{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:23:51Z","timestamp":1760235831091,"version":"build-2065373602"},"reference-count":26,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2021,10,3]],"date-time":"2021-10-03T00:00:00Z","timestamp":1633219200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004329","name":"Javna Agencija za Raziskovalno Dejavnost RS","doi-asserted-by":"publisher","award":["P2-0248, J2-2512, J1-1692 and J1-1693"],"award-info":[{"award-number":["P2-0248, J2-2512, J1-1692 and J1-1693"]}],"id":[{"id":"10.13039\/501100004329","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We obtain new results on 3-rainbow domination numbers of generalized Petersen graphs P(6k,k). 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.<\/jats:p>","DOI":"10.3390\/sym13101860","type":"journal-article","created":{"date-parts":[[2021,10,11]],"date-time":"2021-10-11T01:59:47Z","timestamp":1633917587000},"page":"1860","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["On 3-Rainbow Domination Number of Generalized Petersen Graphs P(6k,k)"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9709-8256","authenticated-orcid":false,"given":"Rija","family":"Erve\u0161","sequence":"first","affiliation":[{"name":"FCETEA, University of Maribor, Smetanova Ulica 17, 2000 Maribor, Slovenia"},{"name":"FIS, Ljubljanska Cesta 31a, 8000 Novo Mesto, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6041-1106","authenticated-orcid":false,"given":"Janez","family":"\u017derovnik","sequence":"additional","affiliation":[{"name":"FME, University of Ljubljana, A\u0161ker\u010deva 6, 1000 Ljubljana, Slovenia"},{"name":"Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,10,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/j.endm.2005.06.059","article-title":"Paired-domination of Cartesian products of graphs and rainbow domination","volume":"22","author":"Henning","year":"2005","journal-title":"Electron. 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