{"id":"https://openalex.org/W4250995650","doi":"https://doi.org/10.1002/(sici)1097-0118(199807)28:3<147::aid-jgt4>3.0.co;2-k","title":"Iterated clique graphs with increasing diameters","display_name":"Iterated clique graphs with increasing diameters","publication_year":1998,"publication_date":"1998-07-01","ids":{"openalex":"https://openalex.org/W4250995650","doi":"https://doi.org/10.1002/(sici)1097-0118(199807)28:3<147::aid-jgt4>3.0.co;2-k"},"language":"en","primary_location":{"id":"doi:10.1002/(sici)1097-0118(199807)28:3<147::aid-jgt4>3.0.co;2-k","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199807)28:3<147::aid-jgt4>3.0.co;2-k","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045780223","display_name":"Claudson F. Bornstein","orcid":null},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]},{"id":"https://openalex.org/I74973139","display_name":"Carnegie Mellon University","ror":"https://ror.org/05x2bcf33","country_code":"US","type":"education","lineage":["https://openalex.org/I74973139"]}],"countries":["BR","US"],"is_corresponding":true,"raw_author_name":"Claudson F. Bornstein","raw_affiliation_strings":["Carnegie Mellon University, School of Computer Science, 5000 Forbes Ave., Pittsburgh, PA 15213","Universidade Federal do Rio de Janeiro, Instituto de Matema\u0301tica, NCE and COPPE, Caixa Postal 2324, 20001-970 Rio de Janeiro, RJ, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Carnegie Mellon University, School of Computer Science, 5000 Forbes Ave., Pittsburgh, PA 15213","institution_ids":["https://openalex.org/I74973139"]},{"raw_affiliation_string":"Universidade Federal do Rio de Janeiro, Instituto de Matema\u0301tica, NCE and COPPE, Caixa Postal 2324, 20001-970 Rio de Janeiro, RJ, Brazil","institution_ids":["https://openalex.org/I122140584"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5004984970","display_name":"Jayme L. Szwarcfiter","orcid":"https://orcid.org/0000-0002-7538-7305"},"institutions":[{"id":"https://openalex.org/I122140584","display_name":"Universidade Federal do Rio de Janeiro","ror":"https://ror.org/03490as77","country_code":"BR","type":"education","lineage":["https://openalex.org/I122140584"]}],"countries":["BR"],"is_corresponding":false,"raw_author_name":"Jayme L. Szwarcfiter","raw_affiliation_strings":["Universidade Federal do Rio de Janeiro, Instituto de Matema\u0301tica, NCE and COPPE, Caixa Postal 2324, 20001-970 Rio de Janeiro, RJ, Brazil"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universidade Federal do Rio de Janeiro, Instituto de Matema\u0301tica, NCE and COPPE, Caixa Postal 2324, 20001-970 Rio de Janeiro, RJ, Brazil","institution_ids":["https://openalex.org/I122140584"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5045780223"],"corresponding_institution_ids":["https://openalex.org/I122140584","https://openalex.org/I74973139"],"apc_list":{"value":4150,"currency":"USD","value_usd":4150},"apc_paid":null,"fwci":0.4888,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.70896552,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"28","issue":"3","first_page":"147","last_page":"154"},"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/T11476","display_name":"Graph theory and applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10829","display_name":"Interconnection Networks and Systems","score":0.9987999796867371,"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":0.8536700010299683},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8256951570510864},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.646865963935852},{"id":"https://openalex.org/keywords/split-graph","display_name":"Split graph","score":0.5577107667922974},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.5356252789497375},{"id":"https://openalex.org/keywords/iterated-function","display_name":"Iterated function","score":0.5308849215507507},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5213871598243713},{"id":"https://openalex.org/keywords/clique-number","display_name":"Clique number","score":0.5063847303390503},{"id":"https://openalex.org/keywords/clique","display_name":"Clique","score":0.47147348523139954},{"id":"https://openalex.org/keywords/simple-graph","display_name":"Simple graph","score":0.4603090286254883},{"id":"https://openalex.org/keywords/chordal-graph","display_name":"Chordal graph","score":0.3640654385089874},{"id":"https://openalex.org/keywords/1-planar-graph","display_name":"1-planar graph","score":0.18767106533050537}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8536700010299683},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8256951570510864},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.646865963935852},{"id":"https://openalex.org/C8554925","wikidata":"https://www.wikidata.org/wiki/Q3893853","display_name":"Split graph","level":5,"score":0.5577107667922974},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5356252789497375},{"id":"https://openalex.org/C140479938","wikidata":"https://www.wikidata.org/wiki/Q5254619","display_name":"Iterated function","level":2,"score":0.5308849215507507},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5213871598243713},{"id":"https://openalex.org/C2985491264","wikidata":"https://www.wikidata.org/wiki/Q761631","display_name":"Clique number","level":3,"score":0.5063847303390503},{"id":"https://openalex.org/C2777035058","wikidata":"https://www.wikidata.org/wiki/Q1662634","display_name":"Clique","level":2,"score":0.47147348523139954},{"id":"https://openalex.org/C2993105083","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Simple graph","level":3,"score":0.4603090286254883},{"id":"https://openalex.org/C160446614","wikidata":"https://www.wikidata.org/wiki/Q1322892","display_name":"Chordal graph","level":3,"score":0.3640654385089874},{"id":"https://openalex.org/C102192266","wikidata":"https://www.wikidata.org/wiki/Q4545823","display_name":"1-planar graph","level":4,"score":0.18767106533050537},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/(sici)1097-0118(199807)28:3<147::aid-jgt4>3.0.co;2-k","is_oa":false,"landing_page_url":"https://doi.org/10.1002/(sici)1097-0118(199807)28:3<147::aid-jgt4>3.0.co;2-k","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W1493037708","https://openalex.org/W4289672287","https://openalex.org/W2972046864","https://openalex.org/W4385327816","https://openalex.org/W2039686598","https://openalex.org/W1995233739","https://openalex.org/W2009862268","https://openalex.org/W4288278989","https://openalex.org/W2888394449","https://openalex.org/W2034795693"],"abstract_inverted_index":{"A":[0],"simple":[1],"argument":[2],"by":[3,15,67,74],"Hedman":[4,26],"shows":[5],"that":[6,20,34,50,97,134],"the":[7,45,81,86,114],"diameter":[8],"of":[9,21,29,47,80,130],"a":[10,30,128],"clique":[11,24],"graph":[12,31],"G":[13,32,132],"differs":[14],"at":[16],"most":[17],"one":[18],"from":[19],"K(G),":[22],"its":[23],"graph.":[25],"described":[27,66],"examples":[28],"such":[33,49,98,133],"diam(K(G))":[35],"=":[36,52,62,89,93,136],"diam(G)":[37,53,137],"+":[38,54,138],"1":[39],"and":[40,70,72,76,91,95],"asked":[41],"in":[42],"general":[43],"about":[44],"existence":[46],"graphs":[48,99,131],"diam(Ki(G))":[51,135],"i.":[55,105,139],"Examples":[56],"satisfying":[57],"this":[58],"equality":[59],"for":[60,101],"i":[61,88,92,108],"2":[63],"have":[64],"been":[65],"Peyrat,":[68],"Rall,":[69],"Slater":[71],"independently":[73],"Balakrishnan":[75],"Paulraja.":[77],"The":[78,106],"authors":[79],"former":[82],"work":[83],"also":[84],"solved":[85],"case":[87],"3":[90],"4":[94],"conjectured":[96],"exist":[100],"every":[102],"positive":[103,123],"integer":[104,124],"cases":[107],"\u2265":[109],"5":[110],"remained":[111],"open.":[112],"In":[113],"present":[115],"article,":[116],"we":[117,126],"prove":[118],"their":[119],"conjecture.":[120],"For":[121],"each":[122],"i,":[125],"describe":[127],"family":[129],"\u00a9":[140],"1998":[141,152],"John":[142],"Wiley":[143],"&":[144],"Sons,":[145],"Inc.":[146],"J.":[147],"Graph":[148],"Theory":[149],"28:":[150],"147\u2013154,":[151]},"counts_by_year":[{"year":2012,"cited_by_count":1}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2025-10-10T00:00:00"}
