{"id":"https://openalex.org/W3204735808","doi":"https://doi.org/10.3390/sym13101860","title":"On 3-Rainbow Domination Number of Generalized Petersen Graphs P(6k,k)","display_name":"On 3-Rainbow Domination Number of Generalized Petersen Graphs P(6k,k)","publication_year":2021,"publication_date":"2021-10-03","ids":{"openalex":"https://openalex.org/W3204735808","doi":"https://doi.org/10.3390/sym13101860","mag":"3204735808"},"language":"en","primary_location":{"id":"doi:10.3390/sym13101860","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101860","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1860/pdf?version=1633252491","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/10/1860/pdf?version=1633252491","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5059220144","display_name":"Rija Erve\u0161","orcid":"https://orcid.org/0000-0002-9709-8256"},"institutions":[{"id":"https://openalex.org/I37696226","display_name":"University of Maribor","ror":"https://ror.org/01d5jce07","country_code":"SI","type":"education","lineage":["https://openalex.org/I37696226"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Rija Erve\u0161","raw_affiliation_strings":["FCETEA, University of Maribor, Smetanova Ulica 17, 2000 Maribor, Slovenia","FIS, Ljubljanska Cesta 31a, 8000 Novo Mesto, Slovenia"],"raw_orcid":"https://orcid.org/0000-0002-9709-8256","affiliations":[{"raw_affiliation_string":"FCETEA, University of Maribor, Smetanova Ulica 17, 2000 Maribor, Slovenia","institution_ids":["https://openalex.org/I37696226"]},{"raw_affiliation_string":"FIS, Ljubljanska Cesta 31a, 8000 Novo Mesto, Slovenia","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089379545","display_name":"Janez \u017derovnik","orcid":"https://orcid.org/0000-0002-6041-1106"},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]},{"id":"https://openalex.org/I4210106342","display_name":"Institute of Mathematics, Physics, and Mechanics","ror":"https://ror.org/01eb3qa50","country_code":"SI","type":"facility","lineage":["https://openalex.org/I4210106342"]}],"countries":["SI"],"is_corresponding":true,"raw_author_name":"Janez \u017derovnik","raw_affiliation_strings":["FME, University of Ljubljana, A\u0161ker\u010deva 6, 1000 Ljubljana, Slovenia","Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia"],"raw_orcid":"https://orcid.org/0000-0002-6041-1106","affiliations":[{"raw_affiliation_string":"FME, University of Ljubljana, A\u0161ker\u010deva 6, 1000 Ljubljana, Slovenia","institution_ids":["https://openalex.org/I153976015"]},{"raw_affiliation_string":"Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia","institution_ids":["https://openalex.org/I4210106342"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5089379545"],"corresponding_institution_ids":["https://openalex.org/I153976015","https://openalex.org/I4210106342"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.5791,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.71970933,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"13","issue":"10","first_page":"1860","last_page":"1860"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9639999866485596,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9186000227928162,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/rainbow","display_name":"Rainbow","score":0.9391666054725647},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.7963156700134277},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7629988193511963},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.629917562007904},{"id":"https://openalex.org/keywords/cardinality","display_name":"Cardinality (data modeling)","score":0.628291130065918},{"id":"https://openalex.org/keywords/singleton","display_name":"Singleton","score":0.5262531638145447},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3573603332042694},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.191386878490448},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.142258882522583},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.13189232349395752},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.10448992252349854}],"concepts":[{"id":"https://openalex.org/C2776558979","wikidata":"https://www.wikidata.org/wiki/Q1052","display_name":"Rainbow","level":2,"score":0.9391666054725647},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.7963156700134277},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7629988193511963},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.629917562007904},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.628291130065918},{"id":"https://openalex.org/C117354338","wikidata":"https://www.wikidata.org/wiki/Q1165112","display_name":"Singleton","level":3,"score":0.5262531638145447},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3573603332042694},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.191386878490448},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.142258882522583},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.13189232349395752},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.10448992252349854},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.0},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.0},{"id":"https://openalex.org/C2779234561","wikidata":"https://www.wikidata.org/wiki/Q11995","display_name":"Pregnancy","level":2,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.3390/sym13101860","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101860","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1860/pdf?version=1633252491","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:d.cobiss.net/repository/si:79263747","is_oa":false,"landing_page_url":"https://plus.cobiss.net/cobiss/si/en/bib/79263747","pdf_url":null,"source":{"id":"https://openalex.org/S7407055177","display_name":"dCOBISS.SI Digital Repository","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"COBISS-ID: 517592345","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:e0e060a739554592b31832a6c83fd139","is_oa":true,"landing_page_url":"https://doaj.org/article/e0e060a739554592b31832a6c83fd139","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 13, Iss 10, p 1860 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/10/1860/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13101860","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13101860","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13101860","pdf_url":"https://www.mdpi.com/2073-8994/13/10/1860/pdf?version=1633252491","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G6199679070","display_name":null,"funder_award_id":"J1-1692","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G687484027","display_name":null,"funder_award_id":"P2-0248","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G7063099000","display_name":null,"funder_award_id":"J2-2512","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G8832944854","display_name":null,"funder_award_id":"P2-0248, J2-2512, J1-1692 and J1-1693","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G8835988220","display_name":null,"funder_award_id":"J1-1693","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3204735808.pdf","grobid_xml":"https://content.openalex.org/works/W3204735808.grobid-xml"},"referenced_works_count":26,"referenced_works":["https://openalex.org/W940747629","https://openalex.org/W1557513888","https://openalex.org/W1968103577","https://openalex.org/W1976768565","https://openalex.org/W1983482338","https://openalex.org/W1987743836","https://openalex.org/W2003370404","https://openalex.org/W2018464213","https://openalex.org/W2024186835","https://openalex.org/W2058200262","https://openalex.org/W2070745899","https://openalex.org/W2154705857","https://openalex.org/W2536500162","https://openalex.org/W2605362387","https://openalex.org/W2795805246","https://openalex.org/W2898860148","https://openalex.org/W2901094222","https://openalex.org/W2911597308","https://openalex.org/W2991317317","https://openalex.org/W2997432480","https://openalex.org/W3013373830","https://openalex.org/W3020823169","https://openalex.org/W3036717146","https://openalex.org/W3128894081","https://openalex.org/W3162235575","https://openalex.org/W6776871794"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W747331120","https://openalex.org/W2997432480","https://openalex.org/W2122516110","https://openalex.org/W2024249013","https://openalex.org/W3112454003","https://openalex.org/W2314466759","https://openalex.org/W2898649000","https://openalex.org/W24519920","https://openalex.org/W2087778462"],"abstract_inverted_index":{"We":[0,38],"obtain":[1],"new":[2],"results":[3,58],"on":[4],"3-rainbow":[5],"domination":[6],"numbers":[7],"of":[8,63],"generalized":[9],"Petersen":[10],"graphs":[11],"P(6k,k).":[12],"In":[13],"some":[14,17],"cases,":[15,27],"for":[16,59],"infinite":[18],"families,":[19],"exact":[20],"values":[21],"are":[22,36],"established;":[23],"in":[24],"all":[25],"other":[26],"the":[28,45],"lower":[29],"and":[30,55],"upper":[31],"bounds":[32],"with":[33],"small":[34],"gaps":[35],"given.":[37],"also":[39],"define":[40],"singleton":[41],"rainbow":[42,64],"domination,":[43],"where":[44],"sets":[46],"assigned":[47],"have":[48],"a":[49],"cardinality":[50],"of,":[51],"at":[52],"most,":[53],"one,":[54],"provide":[56],"analogous":[57],"this":[60],"special":[61],"case":[62],"domination.":[65]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-07-12T07:33:03.550515","created_date":"2021-10-11T00:00:00"}