{"id":"https://openalex.org/W1822118105","doi":"https://doi.org/10.37236/536","title":"The Complexity of Obtaining a Distance-Balanced Graph","display_name":"The Complexity of Obtaining a Distance-Balanced Graph","publication_year":2011,"publication_date":"2011-02-28","ids":{"openalex":"https://openalex.org/W1822118105","doi":"https://doi.org/10.37236/536","mag":"1822118105"},"language":"en","primary_location":{"id":"doi:10.37236/536","is_oa":true,"landing_page_url":"https://doi.org/10.37236/536","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p49/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/v18i1p49/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5034923438","display_name":"Sergio Cabello","orcid":"https://orcid.org/0000-0002-3183-4126"},"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":"Sergio Cabello","raw_affiliation_strings":["University of Ljubljana"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Ljubljana","institution_ids":["https://openalex.org/I153976015"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026692961","display_name":"Primo\u017e Luk\u0161i\u010d","orcid":null},"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":"Primo\u017e Luk\u0161i\u010d","raw_affiliation_strings":["University of Ljubljana"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Ljubljana","institution_ids":["https://openalex.org/I153976015"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.3045,"has_fulltext":true,"cited_by_count":26,"citation_normalized_percentile":{"value":0.78712654,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"18","issue":"1","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":0.9998999834060669,"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/T10374","display_name":"Advanced Graph Theory Research","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"}},{"id":"https://openalex.org/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9995999932289124,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9994000196456909,"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/combinatorics","display_name":"Combinatorics","score":0.8501240015029907},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7938039302825928},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5564925670623779},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4915033280849457},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4422629177570343},{"id":"https://openalex.org/keywords/distance","display_name":"Distance","score":0.41855210065841675}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8501240015029907},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7938039302825928},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5564925670623779},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4915033280849457},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4422629177570343},{"id":"https://openalex.org/C54385418","wikidata":"https://www.wikidata.org/wiki/Q2742711","display_name":"Distance","level":4,"score":0.41855210065841675},{"id":"https://openalex.org/C22590252","wikidata":"https://www.wikidata.org/wiki/Q1058754","display_name":"Shortest path problem","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/536","is_oa":true,"landing_page_url":"https://doi.org/10.37236/536","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p49/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"}],"best_oa_location":{"id":"doi:10.37236/536","is_oa":true,"landing_page_url":"https://doi.org/10.37236/536","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v18i1p49/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":[{"id":"https://openalex.org/G3894112125","display_name":null,"funder_award_id":"P1-0297","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G4217117016","display_name":null,"funder_award_id":"P1-0294","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1822118105.pdf","grobid_xml":"https://content.openalex.org/works/W1822118105.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W125509687","https://openalex.org/W1525605957","https://openalex.org/W1601278659","https://openalex.org/W1989633733","https://openalex.org/W2003204205","https://openalex.org/W2056944495","https://openalex.org/W2081060637","https://openalex.org/W2112825968","https://openalex.org/W2127091615","https://openalex.org/W2134825736","https://openalex.org/W2295733696","https://openalex.org/W2340149117","https://openalex.org/W2486337743","https://openalex.org/W2603607199","https://openalex.org/W2799004609","https://openalex.org/W2988480584","https://openalex.org/W2998757566","https://openalex.org/W4285719527","https://openalex.org/W6676880409","https://openalex.org/W6680140589"],"related_works":["https://openalex.org/W2980963558","https://openalex.org/W2002282073","https://openalex.org/W1882246857","https://openalex.org/W3103304230","https://openalex.org/W2185360082","https://openalex.org/W1992365905","https://openalex.org/W4287664878","https://openalex.org/W3212023493","https://openalex.org/W2790190308","https://openalex.org/W4301046126"],"abstract_inverted_index":{"An":[0,34],"unweighted,":[1],"connected":[2,36],"graph":[3,37],"is":[4,32,38,93],"distance-balanced":[5,40,86],"(also":[6,41],"called":[7,42],"self-median)":[8],"if":[9,45],"there":[10,46,56],"exists":[11],"a":[12,73,84],"number":[13,79],"$d$":[14],"such":[15,50],"that,":[16,51],"for":[17,52,95,127],"any":[18,53],"vertex":[19,54],"$v$,":[20,55],"the":[21,24,68,76,91,102,119],"sum":[22],"of":[23,80,97,129],"distances":[25],"from":[26,64],"$v$":[27],"to":[28,82],"all":[29],"other":[30],"vertices":[31,60],"$d$.":[33],"unweighted":[35],"strongly":[39],"distance-degree":[43],"regular)":[44],"exist":[47],"numbers":[48],"$d_1,d_2,d_3,\\dots$":[49],"are":[57],"precisely":[58],"$d_k$":[59],"at":[61],"distance":[62],"$k$":[63],"$v$.":[65],"We":[66,88],"consider":[67],"following":[69],"optimization":[70],"problem:":[71],"given":[72],"graph,":[74],"add":[75],"minimum":[77],"possible":[78],"edges":[81],"obtain":[83],"(strongly)":[85],"graph.":[87],"show":[89,117],"that":[90,118],"problem":[92,120],"NP-hard":[94],"graphs":[96,128],"diameter":[98,130],"three,":[99],"thus":[100],"answering":[101],"question":[103],"posed":[104],"by":[105],"Jerebic":[106],"et":[107],"al.":[108],"[Distance-balanced":[109],"graphs;":[110],"Ann.":[111],"Comb.":[112],"2008].":[113],"In":[114],"contrast,":[115],"we":[116],"can":[121],"be":[122],"solved":[123],"in":[124],"polynomial":[125],"time":[126],"2.":[131]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2014,"cited_by_count":2},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
