{"id":"https://openalex.org/W2996249744","doi":"https://doi.org/10.23638/dmtcs-21-4-18","title":"Power domination in maximal planar graphs","display_name":"Power domination in maximal planar graphs","publication_year":2019,"publication_date":"2019-12-13","ids":{"openalex":"https://openalex.org/W2996249744","doi":"https://doi.org/10.23638/dmtcs-21-4-18","mag":"2996249744"},"language":"en","primary_location":{"id":"doi:10.23638/dmtcs-21-4-18","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-4-18","pdf_url":"https://dmtcs.episciences.org/5967/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 &amp; Theoretical Computer Science","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://dmtcs.episciences.org/5967/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5038490437","display_name":"Paul Dorbec","orcid":"https://orcid.org/0009-0007-1179-6082"},"institutions":[{"id":"https://openalex.org/I4210105918","display_name":"Normandie Universit\u00e9","ror":"https://ror.org/01k40cz91","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918"]},{"id":"https://openalex.org/I98702875","display_name":"Universit\u00e9 de Caen Normandie","ror":"https://ror.org/051kpcy16","country_code":"FR","type":"education","lineage":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Paul Dorbec","raw_affiliation_strings":["Universit\u00e9 de Caen Normandie"],"raw_orcid":"https://orcid.org/0009-0007-1179-6082","affiliations":[{"raw_affiliation_string":"Universit\u00e9 de Caen Normandie","institution_ids":["https://openalex.org/I4210105918","https://openalex.org/I98702875"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101504239","display_name":"Antonio Gonz\u00e1lez","orcid":"https://orcid.org/0000-0002-2137-5835"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Antonio Gonz\u00e1lez","raw_affiliation_strings":["Department of Didactics of Mathematics, Faculty of Educational Sciences, Universidad de Sevilla","Universidad de Sevilla / University of Sevilla","Universidad de Sevilla = University of Seville"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Didactics of Mathematics, Faculty of Educational Sciences, Universidad de Sevilla","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Universidad de Sevilla / University of Sevilla","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Universidad de Sevilla = University of Seville","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029498919","display_name":"Claire Pennarun","orcid":"https://orcid.org/0000-0002-9895-3437"},"institutions":[{"id":"https://openalex.org/I4210142254","display_name":"Laboratoire Bordelais de Recherche en Informatique","ror":"https://ror.org/03adqg323","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I15057530","https://openalex.org/I4210142254","https://openalex.org/I4210159245","https://openalex.org/I4210160189"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Claire Pennarun","raw_affiliation_strings":["Laboratoire Bordelais de Recherche en Informatique","LaBRI -\n Laboratoire Bordelais de Recherche en Informatique"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire Bordelais de Recherche en Informatique","institution_ids":["https://openalex.org/I4210142254"]},{"raw_affiliation_string":"LaBRI -\n Laboratoire Bordelais de Recherche en Informatique","institution_ids":["https://openalex.org/I4210142254"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5038490437"],"corresponding_institution_ids":["https://openalex.org/I4210105918","https://openalex.org/I98702875"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.20755835,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"vol. 21 no. 4","issue":"Graph Theory","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":0.9944000244140625,"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":0.9944000244140625,"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":0.9778000116348267,"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/T10246","display_name":"Mobile Ad Hoc Networks","score":0.9503999948501587,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/dominating-set","display_name":"Dominating set","score":0.7889748215675354},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7887340188026428},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.7613129615783691},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.7221764326095581},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.6146219372749329},{"id":"https://openalex.org/keywords/domination-analysis","display_name":"Domination analysis","score":0.5879024267196655},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.4970305263996124},{"id":"https://openalex.org/keywords/planar","display_name":"Planar","score":0.4371933341026306},{"id":"https://openalex.org/keywords/power-set","display_name":"Power set","score":0.41212621331214905},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.39983272552490234},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3918374478816986},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.10844948887825012}],"concepts":[{"id":"https://openalex.org/C146661039","wikidata":"https://www.wikidata.org/wiki/Q2915204","display_name":"Dominating set","level":4,"score":0.7889748215675354},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7887340188026428},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7613129615783691},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.7221764326095581},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.6146219372749329},{"id":"https://openalex.org/C83833204","wikidata":"https://www.wikidata.org/wiki/Q5290322","display_name":"Domination analysis","level":4,"score":0.5879024267196655},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.4970305263996124},{"id":"https://openalex.org/C134786449","wikidata":"https://www.wikidata.org/wiki/Q3391255","display_name":"Planar","level":2,"score":0.4371933341026306},{"id":"https://openalex.org/C100643331","wikidata":"https://www.wikidata.org/wiki/Q205170","display_name":"Power set","level":3,"score":0.41212621331214905},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.39983272552490234},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3918374478816986},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.10844948887825012},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.23638/dmtcs-21-4-18","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-4-18","pdf_url":"https://dmtcs.episciences.org/5967/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 &amp; Theoretical Computer Science","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-01550353v3","is_oa":true,"landing_page_url":"https://hal.science/hal-01550353","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":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Discrete Mathematics and Theoretical Computer Science, 2019, vol. 21 no. 4, &#x27E8;10.23638/DMTCS-21-4-18&#x27E9;","raw_type":"Journal articles"},{"id":"pmh:oai:doaj.org/article:f266aa89794e4037a80e0bc90b97966f","is_oa":true,"landing_page_url":"https://doaj.org/article/f266aa89794e4037a80e0bc90b97966f","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":"Discrete Mathematics & Theoretical Computer Science, Vol vol. 21 no. 4, Iss Graph Theory (2019)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.23638/dmtcs-21-4-18","is_oa":true,"landing_page_url":"https://doi.org/10.23638/dmtcs-21-4-18","pdf_url":"https://dmtcs.episciences.org/5967/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 &amp; Theoretical Computer Science","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W2996249744.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1488639514","https://openalex.org/W1963689799","https://openalex.org/W1964514587","https://openalex.org/W1968626979","https://openalex.org/W1981421358","https://openalex.org/W1983156760","https://openalex.org/W1983461314","https://openalex.org/W1995497993","https://openalex.org/W2008586686","https://openalex.org/W2012624063","https://openalex.org/W2013358561","https://openalex.org/W2014504176","https://openalex.org/W2023728975","https://openalex.org/W2039168577","https://openalex.org/W2045704027","https://openalex.org/W2056104224","https://openalex.org/W2063463798","https://openalex.org/W2077014186","https://openalex.org/W2083575592","https://openalex.org/W2162765501","https://openalex.org/W2423480771","https://openalex.org/W2899292663","https://openalex.org/W4240833309","https://openalex.org/W4244025688","https://openalex.org/W4253253982"],"related_works":["https://openalex.org/W2963404550","https://openalex.org/W30750922","https://openalex.org/W2033190383","https://openalex.org/W4299822763","https://openalex.org/W2339280209","https://openalex.org/W4235356280","https://openalex.org/W2763279932","https://openalex.org/W4283726592","https://openalex.org/W3118953946","https://openalex.org/W2564248630"],"abstract_inverted_index":{"Power":[0],"domination":[1,30,109],"in":[2,19],"graphs":[3],"emerged":[4],"from":[5],"the":[6,20,33,51,58,96,115],"problem":[7],"of":[8,29,35,45,47,53,95,102,111,118,133,143],"monitoring":[9],"an":[10],"electrical":[11],"system":[12,21],"by":[13],"placing":[14],"as":[15,22],"few":[16],"measurement":[17,38],"devices":[18,39],"possible.":[23],"It":[24],"corresponds":[25],"to":[26,89],"a":[27,42,48,74,91,112,119,139],"variant":[28],"that":[31,128],"includes":[32],"possibility":[34],"propagation.":[36],"For":[37],"placed":[40],"on":[41],"set":[43,52,59,85,94,142],"S":[44,60,86],"vertices":[46,55,101],"graph":[49,97,113,132],"G,":[50],"monitored":[54,70],"is":[56,87,114],"initially":[57],"together":[61],"with":[62],"all":[63,100],"its":[64],"neighbors.":[65],"Then":[66],"iteratively,":[67],"whenever":[68],"some":[69],"vertex":[71],"v":[72],"has":[73],"single":[75],"neighbor":[76],"u":[77,81],"not":[78],"yet":[79],"monitored,":[80],"gets":[82],"monitored.":[83,106],"A":[84],"said":[88],"be":[90],"power":[92,108,120,140],"dominating":[93,121,141],"G":[98,103],"if":[99],"eventually":[104],"are":[105],"The":[107],"number":[110],"minimum":[116],"size":[117,144],"set.":[122],"In":[123],"this":[124],"paper,":[125],"we":[126],"prove":[127],"any":[129],"maximal":[130],"planar":[131],"order":[134],"n":[135],"\u2265":[136],"6":[137],"admits":[138],"at":[145],"most":[146],"(n\u22122)/4":[147],".":[148]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}
