{"id":"https://openalex.org/W2114713753","doi":"https://doi.org/10.37236/302","title":"Extremal Graph Theory for Metric Dimension and Diameter","display_name":"Extremal Graph Theory for Metric Dimension and Diameter","publication_year":2010,"publication_date":"2010-02-22","ids":{"openalex":"https://openalex.org/W2114713753","doi":"https://doi.org/10.37236/302","mag":"2114713753"},"language":"en","primary_location":{"id":"doi:10.37236/302","is_oa":true,"landing_page_url":"https://doi.org/10.37236/302","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r30/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/v17i1r30/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5088437579","display_name":"Carmen Hernando","orcid":"https://orcid.org/0000-0002-3864-6566"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Carmen Hernando","raw_affiliation_strings":["Universitat Politecnica de Catalunya (Polytechnic University of Catalonia)"],"affiliations":[{"raw_affiliation_string":"Universitat Politecnica de Catalunya (Polytechnic University of Catalonia)","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5021518367","display_name":"Merc\u00e8 Ferrater Mora","orcid":"https://orcid.org/0000-0001-6923-0320"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Merc\u00e8 Mora","raw_affiliation_strings":["Universitat Politecnica de Catalunya (Polytechnic University of Catalonia)"],"affiliations":[{"raw_affiliation_string":"Universitat Politecnica de Catalunya (Polytechnic University of Catalonia)","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5055837693","display_name":"Ignacio M. Pelayo","orcid":"https://orcid.org/0000-0002-6523-0611"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ignacio M. Pelayo","raw_affiliation_strings":["Universitat Politecnica de Catalunya (Polytechnic University of Catalonia)"],"affiliations":[{"raw_affiliation_string":"Universitat Politecnica de Catalunya (Polytechnic University of Catalonia)","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062044790","display_name":"Carlos Seara","orcid":"https://orcid.org/0000-0002-0095-1725"},"institutions":[{"id":"https://openalex.org/I9617848","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31","country_code":"ES","type":"education","lineage":["https://openalex.org/I9617848"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Carlos Seara","raw_affiliation_strings":["Universitat Politecnica de Catalunya (Polytechnic University of Catalonia)"],"affiliations":[{"raw_affiliation_string":"Universitat Politecnica de Catalunya (Polytechnic University of Catalonia)","institution_ids":["https://openalex.org/I9617848"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066302647","display_name":"David R. Wood","orcid":"https://orcid.org/0000-0001-8866-3041"},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"David R. Wood","raw_affiliation_strings":["University of Melbourne"],"affiliations":[{"raw_affiliation_string":"University of Melbourne","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5088437579"],"corresponding_institution_ids":["https://openalex.org/I9617848"],"apc_list":null,"apc_paid":null,"fwci":12.412,"has_fulltext":true,"cited_by_count":187,"citation_normalized_percentile":{"value":0.99087489,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":98,"max":100},"biblio":{"volume":"17","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998999834060669,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9998999834060669,"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":0.9055779576301575},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8550024032592773},{"id":"https://openalex.org/keywords/metric-dimension","display_name":"Metric dimension","score":0.7169142961502075},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6256791353225708},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5560947060585022},{"id":"https://openalex.org/keywords/beta","display_name":"BETA (programming language)","score":0.5021967887878418},{"id":"https://openalex.org/keywords/connectivity","display_name":"Connectivity","score":0.4336736798286438},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.39089879393577576},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.10925841331481934},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.05183136463165283}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.9055779576301575},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8550024032592773},{"id":"https://openalex.org/C60933471","wikidata":"https://www.wikidata.org/wiki/Q17152964","display_name":"Metric dimension","level":5,"score":0.7169142961502075},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6256791353225708},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5560947060585022},{"id":"https://openalex.org/C2776174256","wikidata":"https://www.wikidata.org/wiki/Q830842","display_name":"BETA (programming language)","level":2,"score":0.5021967887878418},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.4336736798286438},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39089879393577576},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.10925841331481934},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.05183136463165283},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"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":5,"locations":[{"id":"doi:10.37236/302","is_oa":true,"landing_page_url":"https://doi.org/10.37236/302","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r30/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:recercat.cat:2072/190278","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/8382","pdf_url":null,"source":{"id":"https://openalex.org/S4306402147","display_name":"RECERCAT (Consorci de Serveis Universitaris de Catalunya)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210090028","host_organization_name":"Consorci de Serveis Universitaris de Catalunya","host_organization_lineage":["https://openalex.org/I4210090028"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:dnet:upcommonspor::ec6105775e43763e279dabf2bbdc83e0","is_oa":true,"landing_page_url":"http://hdl.handle.net/2117/8261","pdf_url":"https://upcommons.upc.edu/bitstream/2117/8261/1/extremal.pdf","source":{"id":"https://openalex.org/S4306402641","display_name":"LA Referencia (Red Federada de Repositorios Institucionales de Publicaciones Cient\u00edficas)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4383465926","host_organization_name":"LA Referencia","host_organization_lineage":["https://openalex.org/I4383465926"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:upcommons.upc.edu:2117/8261","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/8261","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:upcommons.upc.edu:2117/8382","is_oa":true,"landing_page_url":"https://hdl.handle.net/2117/8382","pdf_url":null,"source":{"id":"https://openalex.org/S4210207057","display_name":"QRU Quaderns de Recerca en Urbanisme","issn_l":"2014-9689","issn":["2014-9689","2385-6777"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310322448","host_organization_name":"Q71272178","host_organization_lineage":["https://openalex.org/P4310322448"],"host_organization_lineage_names":["Q71272178"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.37236/302","is_oa":true,"landing_page_url":"https://doi.org/10.37236/302","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v17i1r30/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":[{"id":"https://openalex.org/F4320321837","display_name":"Ministerio de Econom\u00eda y Competitividad","ror":"https://ror.org/034900433"},{"id":"https://openalex.org/F4320328447","display_name":"Universitat Polit\u00e8cnica de Catalunya","ror":"https://ror.org/03mb6wj31"},{"id":"https://openalex.org/F4320335162","display_name":"Departament d'Universitats, Recerca i Societat de la Informaci\u00f3","ror":null}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2114713753.pdf","grobid_xml":"https://content.openalex.org/works/W2114713753.grobid-xml"},"referenced_works_count":31,"referenced_works":["https://openalex.org/W77791873","https://openalex.org/W109448701","https://openalex.org/W141587127","https://openalex.org/W1958462902","https://openalex.org/W1966929086","https://openalex.org/W1973911938","https://openalex.org/W1982269548","https://openalex.org/W2002199085","https://openalex.org/W2008786622","https://openalex.org/W2015569852","https://openalex.org/W2026014023","https://openalex.org/W2037298352","https://openalex.org/W2056716143","https://openalex.org/W2074389465","https://openalex.org/W2085331602","https://openalex.org/W2086552038","https://openalex.org/W2102189646","https://openalex.org/W2105232761","https://openalex.org/W2108442028","https://openalex.org/W2324588684","https://openalex.org/W2582595341","https://openalex.org/W2590190411","https://openalex.org/W2591601145","https://openalex.org/W2592828425","https://openalex.org/W2750544743","https://openalex.org/W2990034176","https://openalex.org/W4238361102","https://openalex.org/W4241834812","https://openalex.org/W4245623919","https://openalex.org/W4285719527","https://openalex.org/W6603159187"],"related_works":["https://openalex.org/W4313216298","https://openalex.org/W2071797893","https://openalex.org/W2097063382","https://openalex.org/W2037298352","https://openalex.org/W4390529299","https://openalex.org/W2384431448","https://openalex.org/W3002741190","https://openalex.org/W2884117239","https://openalex.org/W2188756358","https://openalex.org/W3189256254"],"abstract_inverted_index":{"A":[0],"set":[1,38,46],"of":[2,19,29,35,39,47,63,75,92,116,125],"vertices":[3,23],"$S$":[4],"resolves":[5],"a":[6,36,64,97,117,130],"connected":[7],"graph":[8,65,118],"$G$":[9,30],"if":[10],"every":[11],"vertex":[12],"is":[13,31,57,69,78,110],"uniquely":[14],"determined":[15],"by":[16],"its":[17],"vector":[18],"distances":[20],"to":[21,79,111],"the":[22,32,45,60,81,113],"in":[24,66,83,119],"$S$.":[25],"The":[26,72,107],"metric":[27,50],"dimension":[28,51],"minimum":[33,61],"cardinality":[34],"resolving":[37],"$G$.":[40],"Let":[41],"${\\cal":[42,67,84,120],"G}_{\\beta,D}$":[43,68,85,121],"be":[44],"graphs":[48,82],"with":[49,86],"$\\beta$":[52,93],"and":[53,94,127],"diameter":[54],"$D$.":[55,95],"It":[56],"well-known":[58],"that":[59],"order":[62,87,115],"exactly":[70],"$\\beta+D$.":[71],"first":[73],"contribution":[74,109],"this":[76],"paper":[77],"characterise":[80],"$\\beta+D$":[88],"for":[89,103,122],"all":[90,123],"values":[91,124],"Such":[96],"characterisation":[98],"was":[99,134],"previously":[100,135],"only":[101],"known":[102],"$D\\leq2$":[104],"or":[105],"$\\beta\\leq1$.":[106],"second":[108],"determine":[112],"maximum":[114],"$D$":[126],"$\\beta$.":[128],"Only":[129],"weak":[131],"upper":[132],"bound":[133],"known.":[136]},"counts_by_year":[{"year":2026,"cited_by_count":5},{"year":2025,"cited_by_count":15},{"year":2024,"cited_by_count":5},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":26},{"year":2020,"cited_by_count":14},{"year":2019,"cited_by_count":10},{"year":2018,"cited_by_count":12},{"year":2017,"cited_by_count":7},{"year":2016,"cited_by_count":8},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":11},{"year":2013,"cited_by_count":16},{"year":2012,"cited_by_count":16}],"updated_date":"2026-03-21T08:13:44.787528","created_date":"2025-10-10T00:00:00"}
