{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T02:00:55Z","timestamp":1760234455876,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,5,6]],"date-time":"2021-05-06T00:00:00Z","timestamp":1620259200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>We obtain new results on 2-rainbow domination number of generalized Petersen graphs P(5k,k). In some cases (for some infinite families), exact values are established, and in all other cases lower and upper bounds are given. In particular, it is shown that, for k&gt;3, \u03b3r2(P(5k,k))=4k for k\u22612,8mod10, \u03b3r2(P(5k,k))=4k+1 for k\u22615,9mod10, 4k+1\u2264\u03b3r2(P(5k,k))\u22644k+2 for k\u22611,6,7mod10, and 4k+1\u2264\u03b3r2(P(5k,k))\u22644k+3 for k\u22610,3,4mod10.<\/jats:p>","DOI":"10.3390\/sym13050809","type":"journal-article","created":{"date-parts":[[2021,5,7]],"date-time":"2021-05-07T22:36:24Z","timestamp":1620426984000},"page":"809","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["On 2-Rainbow Domination Number of Generalized Petersen Graphs P(5k,k)"],"prefix":"10.3390","volume":"13","author":[{"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":[[2021,5,6]]},"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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