{"id":"https://openalex.org/W2898950301","doi":"https://doi.org/10.23638/dmtcs-21-1-9","title":"The 2-domination and Roman domination numbers of grid graphs","display_name":"The 2-domination and Roman domination numbers of grid graphs","publication_year":2019,"publication_date":"2019-05-23","ids":{"openalex":"https://openalex.org/W2898950301","doi":"https://doi.org/10.23638/dmtcs-21-1-9","mag":"2898950301"},"language":"en","primary_location":{"id":"doi:10.23638/dmtcs-21-1-9","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-1-9","pdf_url":"https://dmtcs.episciences.org/5482/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},"type":"preprint","indexed_in":["arxiv","crossref","datacite","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dmtcs.episciences.org/5482/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5102487549","display_name":"Micha\u00ebl Rao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Micha\u00ebl Rao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5061685796","display_name":"Alexandre Talon","orcid":"https://orcid.org/0000-0002-6127-3796"},"institutions":[{"id":"https://openalex.org/I4210144566","display_name":"Laboratoire de l'Informatique du Parall\u00e9lisme","ror":"https://ror.org/04msnz457","country_code":"FR","type":"facility","lineage":["https://openalex.org/I100532134","https://openalex.org/I113428412","https://openalex.org/I1294671590","https://openalex.org/I1326498283","https://openalex.org/I203339264","https://openalex.org/I203339264","https://openalex.org/I4210144566"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Alexandre Talon","raw_affiliation_strings":["Laboratoire de l'Informatique du Parall\u00e9lisme"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de l'Informatique du Parall\u00e9lisme","institution_ids":["https://openalex.org/I4210144566"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6064,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":{"value":0.6894318,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"vol. 21 no. 1, ICGT 2018","issue":null,"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":0.9998000264167786,"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":0.9998000264167786,"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":0.9983999729156494,"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":0.9851999878883362,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/grid","display_name":"Grid","score":0.8239247798919678},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7377634048461914},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.706500768661499},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5256767868995667},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.4896998703479767},{"id":"https://openalex.org/keywords/transfer","display_name":"Transfer (computing)","score":0.45934754610061646},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.4570692777633667},{"id":"https://openalex.org/keywords/grid-cell","display_name":"Grid cell","score":0.4242945909500122},{"id":"https://openalex.org/keywords/value","display_name":"Value (mathematics)","score":0.4181155860424042},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.38615110516548157},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.2766212821006775},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.1060689389705658},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.08771413564682007},{"id":"https://openalex.org/keywords/parallel-computing","display_name":"Parallel computing","score":0.0731218159198761}],"concepts":[{"id":"https://openalex.org/C187691185","wikidata":"https://www.wikidata.org/wiki/Q2020720","display_name":"Grid","level":2,"score":0.8239247798919678},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7377634048461914},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.706500768661499},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5256767868995667},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.4896998703479767},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.45934754610061646},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.4570692777633667},{"id":"https://openalex.org/C2983008078","wikidata":"https://www.wikidata.org/wiki/Q863495","display_name":"Grid cell","level":3,"score":0.4242945909500122},{"id":"https://openalex.org/C2776291640","wikidata":"https://www.wikidata.org/wiki/Q2912517","display_name":"Value (mathematics)","level":2,"score":0.4181155860424042},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.38615110516548157},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.2766212821006775},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.1060689389705658},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.08771413564682007},{"id":"https://openalex.org/C173608175","wikidata":"https://www.wikidata.org/wiki/Q232661","display_name":"Parallel computing","level":1,"score":0.0731218159198761},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":4,"locations":[{"id":"doi:10.23638/dmtcs-21-1-9","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-1-9","pdf_url":"https://dmtcs.episciences.org/5482/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1810.12896","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1810.12896","pdf_url":"https://arxiv.org/pdf/1810.12896","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"pmh:oai:HAL:hal-02289499v1","is_oa":false,"landing_page_url":"https://hal.science/hal-02289499","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"https://dmtcs.episciences.org/5482","raw_type":"Journal articles"},{"id":"doi:10.48550/arxiv.1810.12896","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1810.12896","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article-journal"}],"best_oa_location":{"id":"doi:10.23638/dmtcs-21-1-9","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-1-9","pdf_url":"https://dmtcs.episciences.org/5482/pdf","source":{"id":"https://openalex.org/S200334879","display_name":"Discrete Mathematics & Theoretical Computer Science","issn_l":"1365-8050","issn":["1365-8050","1462-7264"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4328141799","host_organization_name":"French association","host_organization_lineage":["https://openalex.org/P4328141799"],"host_organization_lineage_names":["French association"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Discrete Mathematics & Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2898950301.pdf","grobid_xml":"https://content.openalex.org/works/W2898950301.grobid-xml"},"referenced_works_count":8,"referenced_works":["https://openalex.org/W1590776067","https://openalex.org/W1597381944","https://openalex.org/W2006503776","https://openalex.org/W2086400760","https://openalex.org/W2101183555","https://openalex.org/W2104330975","https://openalex.org/W2580527748","https://openalex.org/W2963377580"],"related_works":["https://openalex.org/W2794522194","https://openalex.org/W2963404550","https://openalex.org/W30750922","https://openalex.org/W4378234127","https://openalex.org/W72870998","https://openalex.org/W2763279932","https://openalex.org/W2339280209","https://openalex.org/W2346500824","https://openalex.org/W4299822763","https://openalex.org/W2033190383"],"abstract_inverted_index":{"We":[0,40,98],"investigate":[1],"the":[2,10,20,27,46,57,75,101,105,126,131],"2-domination":[3,47],"number":[4,48],"for":[5,68,81],"grid":[6,21,28,110],"graphs,":[7],"that":[8,23,123],"is":[9,128],"size":[11],"of":[12,17,19,26,49,77],"a":[13,42],"smallest":[14],"set":[15],"$D$":[16,31],"vertices":[18],"such":[22],"each":[24],"vertex":[25],"belongs":[29],"to":[30,103,125],"or":[32],"has":[33],"at":[34,118],"least":[35],"two":[36],"neighbours":[37],"in":[38,96,130,138],"$D$.":[39],"give":[41],"closed":[43],"formula":[44],"giving":[45],"any":[50],"$n":[51,69,82],"\\!\\times\\!":[52],"m$":[53],"grid,":[54],"hereby":[55],"confirming":[56],"results":[58,127],"found":[59],"by":[60],"Lu":[61],"and":[62,64,72],"Xu,":[63],"Shaheen":[65,78],"et":[66,79],"al.":[67,80],"\\leq":[70],"4$":[71],"slightly":[73],"correct":[74],"value":[76],"=":[83],"5$.":[84],"The":[85,121],"proof":[86],"relies":[87],"on":[88,109],"some":[89],"dynamic":[90],"programming":[91],"algorithms,":[92],"using":[93],"transfer":[94],"matrices":[95],"(min,+)-algebra.":[97],"also":[99],"apply":[100],"method":[102],"solve":[104],"Roman":[106],"domination":[107],"problem":[108],"graphs.":[111],"Comment:":[112],"11":[113],"pages,":[114],"5":[115],"figures,":[116],"presented":[117],"ICGT":[119],"2018":[120],"program":[122],"led":[124],"included":[129],"Source":[132],"directory":[133],"(see":[134],"Other":[135],"formats)":[136],"Accepted":[137],"DMTCS":[139],"vol":[140],"21.":[141],"Journal":[142],"version":[143],"with":[144],"their":[145],"template":[146]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}