{"id":"https://openalex.org/W1597381944","doi":"https://doi.org/10.37236/2595","title":"Roman Domination Number of the Cartesian Products of Paths and Cycles","display_name":"Roman Domination Number of the Cartesian Products of Paths and Cycles","publication_year":2012,"publication_date":"2012-08-09","ids":{"openalex":"https://openalex.org/W1597381944","doi":"https://doi.org/10.37236/2595","mag":"1597381944"},"language":"en","primary_location":{"id":"doi:10.37236/2595","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2595","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p19/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p19/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5072771866","display_name":"Polona Pavli\u010d","orcid":null},"institutions":[{"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":"Polona Pavli\u010d","raw_affiliation_strings":["Institute of Mathematics, Physics and Mechanics"],"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Physics and Mechanics","institution_ids":["https://openalex.org/I4210106342"]}]},{"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"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Janez \u017derovnik","raw_affiliation_strings":["Faculty of Mechanical Engineering, University of Ljubljana"],"affiliations":[{"raw_affiliation_string":"Faculty of Mechanical Engineering, University of Ljubljana","institution_ids":["https://openalex.org/I153976015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5072771866"],"corresponding_institution_ids":["https://openalex.org/I4210106342"],"apc_list":null,"apc_paid":null,"fwci":1.0384,"has_fulltext":true,"cited_by_count":39,"citation_normalized_percentile":{"value":0.75719202,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"19","issue":"3","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9879000186920166,"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":0.9879000186920166,"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/combinatorics","display_name":"Combinatorics","score":0.8588945865631104},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7818528413772583},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.7630327939987183},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6253647804260254},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5204563140869141},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.48437437415122986},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4248931407928467},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4203135371208191},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.3597809672355652},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.345110684633255}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8588945865631104},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7818528413772583},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.7630327939987183},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6253647804260254},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5204563140869141},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.48437437415122986},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4248931407928467},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4203135371208191},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.3597809672355652},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.345110684633255},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/2595","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2595","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p19/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.418.455","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.418.455","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.imfm.si/preprinti/PDF/01165.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/2595","is_oa":true,"landing_page_url":"https://doi.org/10.37236/2595","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v19i3p19/pdf","source":{"id":"https://openalex.org/S38448739","display_name":"The Electronic Journal of Combinatorics","issn_l":"1077-8926","issn":["1077-8926","1097-1440"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310317970","host_organization_name":"Electronic Journal of Combinatorics","host_organization_lineage":["https://openalex.org/P4310317970"],"host_organization_lineage_names":["Electronic Journal of Combinatorics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1597381944.pdf","grobid_xml":"https://content.openalex.org/works/W1597381944.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W1493071618","https://openalex.org/W1519450118","https://openalex.org/W1519556010","https://openalex.org/W1524302676","https://openalex.org/W1531868704","https://openalex.org/W1581552469","https://openalex.org/W1590776067","https://openalex.org/W1963724532","https://openalex.org/W1974016110","https://openalex.org/W1984228559","https://openalex.org/W1989438579","https://openalex.org/W1992801013","https://openalex.org/W1994365837","https://openalex.org/W2000865051","https://openalex.org/W2011469463","https://openalex.org/W2012379512","https://openalex.org/W2013474931","https://openalex.org/W2019578481","https://openalex.org/W2019737201","https://openalex.org/W2031680558","https://openalex.org/W2033170802","https://openalex.org/W2060569445","https://openalex.org/W2071135458","https://openalex.org/W2073661823","https://openalex.org/W2087928776","https://openalex.org/W2088887891","https://openalex.org/W2089633648","https://openalex.org/W2090249824","https://openalex.org/W2101183555","https://openalex.org/W2116916457","https://openalex.org/W2139312684","https://openalex.org/W2158057601","https://openalex.org/W2158959343","https://openalex.org/W2184609083","https://openalex.org/W2275853770","https://openalex.org/W2471604269","https://openalex.org/W2490805901","https://openalex.org/W2580527748","https://openalex.org/W2742043516","https://openalex.org/W2951306406","https://openalex.org/W3123514010","https://openalex.org/W4251005761"],"related_works":["https://openalex.org/W2070745899","https://openalex.org/W2738565459","https://openalex.org/W1464226492","https://openalex.org/W3201378981","https://openalex.org/W2080000226","https://openalex.org/W2794522194","https://openalex.org/W1588305999","https://openalex.org/W2963404550","https://openalex.org/W6227737","https://openalex.org/W2264220954"],"abstract_inverted_index":{"Roman":[0,43,70,93,141],"domination":[1,8,44,71,94],"is":[2,33,46],"an":[3,56,59,64],"historically":[4],"inspired":[5],"variety":[6],"of":[7,51,73,76,96,100,146],"in":[9,11,22,54,143],"graphs,":[10],"which":[12,80],"vertices":[13],"are":[14],"assigned":[15,29,38],"a":[16,24,36],"value":[17,31,40],"from":[18],"the":[19,30,39,47,69,92,97,101],"set":[20],"$\\{0,1,2\\}$":[21],"such":[23,55],"way":[25],"that":[26],"every":[27],"vertex":[28,37],"0":[32],"adjacent":[34],"to":[35],"2.":[41],"The":[42],"number":[45],"minimum":[48],"possible":[49],"sum":[50],"all":[52,137],"values":[53],"assignment.":[57],"Using":[58,85],"algebraic":[60],"approach":[61],"we":[62,88],"present":[63],"$O(C)$-time":[65],"algorithm":[66,87],"for":[67,91,107,120,128],"computing":[68],"numbers":[72,95],"special":[74,138],"classes":[75],"graphs":[77,139,142],"called":[78,140],"polygraphs,":[79],"include":[81],"rotagraphs":[82],"and":[83,109,114,117,123,131],"fasciagraphs.":[84],"this":[86],"determine":[89],"formulas":[90],"Cartesian":[98],"products":[99],"form":[102],"$P_n\\Box":[103,105],"P_k$,":[104],"C_k$,":[106,119],"$k\\leq8$":[108],"$n":[110,124],"\\in":[111,125],"{\\mathbb":[112,126],"N}$,":[113,127],"$C_n\\Box":[115,118],"P_k$":[116],"$k\\leq":[121],"6$":[122],"paths":[129],"$P_n$":[130],"cycles":[132],"$C_n$.":[133],"We":[134],"also":[135],"find":[136],"these":[144],"families":[145],"graphs.":[147]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":7},{"year":2018,"cited_by_count":9},{"year":2017,"cited_by_count":4},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":2}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
