{"id":"https://openalex.org/W2467178344","doi":"https://doi.org/10.37236/6269","title":"Dominating Sequences in Grid-Like and Toroidal Graphs","display_name":"Dominating Sequences in Grid-Like and Toroidal Graphs","publication_year":2016,"publication_date":"2016-12-09","ids":{"openalex":"https://openalex.org/W2467178344","doi":"https://doi.org/10.37236/6269","mag":"2467178344"},"language":"en","primary_location":{"id":"doi:10.37236/6269","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6269","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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://doi.org/10.37236/6269","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089443562","display_name":"Bo\u0161tjan Bre\u0161ar","orcid":"https://orcid.org/0000-0001-8471-4796"},"institutions":[{"id":"https://openalex.org/I4210096574","display_name":"Institute of Mathematics and Mechanics","ror":"https://ror.org/00ab5b586","country_code":"AZ","type":"facility","lineage":["https://openalex.org/I126595936","https://openalex.org/I4210096574"]},{"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"]},{"id":"https://openalex.org/I4210116091","display_name":"Department of Physics, Mathematics and Informatics","ror":"https://ror.org/023sm4k53","country_code":"BY","type":"facility","lineage":["https://openalex.org/I151823869","https://openalex.org/I4210116091"]}],"countries":["AZ","BY","SI"],"is_corresponding":true,"raw_author_name":"Bo\u0161tjan Bre\u0161ar","raw_affiliation_strings":["Faculty of Natural Sciences and Mathematics and \r\nInstitute of Mathematics, Physics and Mechanics","Faculty of Natural Sciences and Mathematics and \nInstitute of Mathematics, Physics and Mechanics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics and \r\nInstitute of Mathematics, Physics and Mechanics","institution_ids":["https://openalex.org/I4210116091","https://openalex.org/I4210096574"]},{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics and \nInstitute of Mathematics, Physics and Mechanics","institution_ids":["https://openalex.org/I4210106342"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085425895","display_name":"Csilla Bujt\u00e1s","orcid":"https://orcid.org/0000-0002-0511-5291"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Csilla Bujt\u00e1s","raw_affiliation_strings":["Department of Computer Science and Systems Technology and\r\nAlfr\u00e9d R\u00e9nyi Institute of Mathematics","Department of Computer Science and Systems Technology and\nAlfr\u00e9d R\u00e9nyi Institute of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Systems Technology and\r\nAlfr\u00e9d R\u00e9nyi Institute of Mathematics","institution_ids":["https://openalex.org/I127817813"]},{"raw_affiliation_string":"Department of Computer Science and Systems Technology and\nAlfr\u00e9d R\u00e9nyi Institute of Mathematics","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113909068","display_name":"Tanja Gologranc","orcid":null},"institutions":[{"id":"https://openalex.org/I4210096574","display_name":"Institute of Mathematics and Mechanics","ror":"https://ror.org/00ab5b586","country_code":"AZ","type":"facility","lineage":["https://openalex.org/I126595936","https://openalex.org/I4210096574"]},{"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"]},{"id":"https://openalex.org/I4210116091","display_name":"Department of Physics, Mathematics and Informatics","ror":"https://ror.org/023sm4k53","country_code":"BY","type":"facility","lineage":["https://openalex.org/I151823869","https://openalex.org/I4210116091"]}],"countries":["AZ","BY","SI"],"is_corresponding":false,"raw_author_name":"Tanja Gologranc","raw_affiliation_strings":["Faculty of Natural Sciences and Mathematics and\r\nInstitute of Mathematics, Physics and Mechanics","Faculty of Natural Sciences and Mathematics and\nInstitute of Mathematics, Physics and Mechanics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics and\r\nInstitute of Mathematics, Physics and Mechanics","institution_ids":["https://openalex.org/I4210116091","https://openalex.org/I4210096574"]},{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics and\nInstitute of Mathematics, Physics and Mechanics","institution_ids":["https://openalex.org/I4210106342"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049148828","display_name":"Sandi Klav\u017ear","orcid":"https://orcid.org/0000-0002-1556-4744"},"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"]},{"id":"https://openalex.org/I4210116091","display_name":"Department of Physics, Mathematics and Informatics","ror":"https://ror.org/023sm4k53","country_code":"BY","type":"facility","lineage":["https://openalex.org/I151823869","https://openalex.org/I4210116091"]}],"countries":["BY","SI"],"is_corresponding":false,"raw_author_name":"Sandi Klav\u017ear","raw_affiliation_strings":["Faculty of Natural Sciences and Mathematics and \r\nInstitute of Mathematics, Physics and Mechanics and\r\nFaculty of Mathematics and Physics","Faculty of Natural Sciences and Mathematics and \nInstitute of Mathematics, Physics and Mechanics and\nFaculty of Mathematics and Physics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics and \r\nInstitute of Mathematics, Physics and Mechanics and\r\nFaculty of Mathematics and Physics","institution_ids":["https://openalex.org/I4210116091"]},{"raw_affiliation_string":"Faculty of Natural Sciences and Mathematics and \nInstitute of Mathematics, Physics and Mechanics and\nFaculty of Mathematics and Physics","institution_ids":["https://openalex.org/I4210106342"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049079943","display_name":"Ga\u0161per Ko\u0161mrlj","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":false,"raw_author_name":"Ga\u0161per Ko\u0161mrlj","raw_affiliation_strings":["Institute of Mathematics, Physics and Mechanics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, Physics and Mechanics","institution_ids":["https://openalex.org/I4210106342"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5049283802","display_name":"Bal\u00e1zs Patk\u00f3s","orcid":"https://orcid.org/0000-0002-1651-2487"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Bal\u00e1zs Patk\u00f3s","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","institution_ids":["https://openalex.org/I127817813"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5026437192","display_name":"\u0179solt Tuza","orcid":"https://orcid.org/0000-0003-3235-9221"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"Zsolt Tuza","raw_affiliation_strings":["Department of Computer Science and Systems Technology and\r\nAlfr\u00e9d R\u00e9nyi Institute of Mathematics","Department of Computer Science and Systems Technology and\nAlfr\u00e9d R\u00e9nyi Institute of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science and Systems Technology and\r\nAlfr\u00e9d R\u00e9nyi Institute of Mathematics","institution_ids":["https://openalex.org/I127817813"]},{"raw_affiliation_string":"Department of Computer Science and Systems Technology and\nAlfr\u00e9d R\u00e9nyi Institute of Mathematics","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5018834142","display_name":"M\u00e1t\u00e9 Vizer","orcid":"https://orcid.org/0000-0002-2360-3918"},"institutions":[{"id":"https://openalex.org/I127817813","display_name":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","ror":"https://ror.org/03vw74f64","country_code":"HU","type":"facility","lineage":["https://openalex.org/I127817813","https://openalex.org/I7597260"]}],"countries":["HU"],"is_corresponding":false,"raw_author_name":"M\u00e1t\u00e9 Vizer","raw_affiliation_strings":["Alfr\u00e9d R\u00e9nyi Institute of Mathematics"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Alfr\u00e9d R\u00e9nyi Institute of Mathematics","institution_ids":["https://openalex.org/I127817813"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5089443562"],"corresponding_institution_ids":["https://openalex.org/I4210096574","https://openalex.org/I4210106342","https://openalex.org/I4210116091"],"apc_list":null,"apc_paid":null,"fwci":1.4418,"has_fulltext":false,"cited_by_count":14,"citation_normalized_percentile":{"value":0.83740196,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"23","issue":"4","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":0.9980999827384949,"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":0.9980999827384949,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9039999842643738,"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/lexicographical-order","display_name":"Lexicographical order","score":0.8747528791427612},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.8703466653823853},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8526462316513062},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8088493347167969},{"id":"https://openalex.org/keywords/cartesian-product","display_name":"Cartesian product","score":0.7295268774032593},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6971121430397034},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5433436632156372},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.452814519405365},{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.4484524726867676},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4384402334690094},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.43572190403938293},{"id":"https://openalex.org/keywords/dominating-set","display_name":"Dominating set","score":0.42570361495018005},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3732772767543793},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.06562173366546631}],"concepts":[{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.8747528791427612},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.8703466653823853},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8526462316513062},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8088493347167969},{"id":"https://openalex.org/C65236422","wikidata":"https://www.wikidata.org/wiki/Q173740","display_name":"Cartesian product","level":2,"score":0.7295268774032593},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6971121430397034},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5433436632156372},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.452814519405365},{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.4484524726867676},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4384402334690094},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.43572190403938293},{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.42570361495018005},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3732772767543793},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.06562173366546631},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"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/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/6269","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6269","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.37236/6269","is_oa":true,"landing_page_url":"https://doi.org/10.37236/6269","pdf_url":null,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W2794522194","https://openalex.org/W1464226492","https://openalex.org/W2963404550","https://openalex.org/W2738565459","https://openalex.org/W2054696976","https://openalex.org/W30750922","https://openalex.org/W2033190383","https://openalex.org/W4235356280","https://openalex.org/W4299822763","https://openalex.org/W2235657338"],"abstract_inverted_index":{"A":[0],"longest":[1],"sequence":[2],"$S$":[3,16,37],"of":[4,7,15,36,43,72,107,118],"distinct":[5],"vertices":[6],"a":[8,30,77],"graph":[9,58],"$G$":[10],"such":[11],"that":[12,20],"each":[13,71],"vertex":[14,19],"dominates":[17],"some":[18],"is":[21,28,38,96],"not":[22],"dominated":[23],"by":[24],"its":[25],"preceding":[26],"vertices,":[27],"called":[29],"Grundy":[31,40,51,82,111],"dominating":[32],"sequence;":[33],"the":[34,39,50,55,60,62,64,67,73,81,92,102,108],"length":[35],"domination":[41,52,83,112],"number":[42,53,84],"$G$.":[44],"In":[45,105],"this":[46],"paper":[47],"we":[48,75],"study":[49],"in":[54],"four":[56],"standard":[57],"products:":[59],"Cartesian,":[61],"lexicographic,":[63],"direct,":[65],"and":[66,95],"strong":[68,103],"product.":[69,104],"For":[70],"products":[74,117],"present":[76],"lower":[78],"bound":[79],"for":[80,91,101,116],"which":[85],"turns":[86],"out":[87],"to":[88,98],"be":[89,99],"exact":[90,100,110],"lexicographic":[93],"product":[94],"conjectured":[97],"most":[106],"cases":[109],"numbers":[113],"are":[114],"determined":[115],"paths":[119],"and/or":[120],"cycles.":[121]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":5},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}