{"id":"https://openalex.org/W4251292291","doi":"https://doi.org/10.1002/(sici)1097-0118(199908)31:4<283::aid-jgt3>3.0.co;2-h","title":"(n,e)-graphs with maximum sum of squares of degrees","display_name":"(n,e)-graphs with maximum sum of squares of degrees","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W4251292291","doi":"https://doi.org/10.1002/(sici)1097-0118(199908)31:4<283::aid-jgt3>3.0.co;2-h"},"language":"en","primary_location":{"id":"pmh:oai:iris.uniroma1.it:11573/245353","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/245353","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"},"type":"article","indexed_in":[],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"PELED U.","orcid":null},"institutions":[{"id":"https://openalex.org/I39422238","display_name":"University of Illinois Chicago","ror":"https://ror.org/02mpq6x41","country_code":"US","type":"education","lineage":["https://openalex.org/I39422238"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"PELED U.","raw_affiliation_strings":["University of Illinois at Chicago, Chicago, Illinois"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois at Chicago, Chicago, Illinois","institution_ids":["https://openalex.org/I39422238"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5019855296","display_name":"Rossella Petreschi","orcid":"https://orcid.org/0000-0001-6972-2106"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"PETRESCHI, Rossella","raw_affiliation_strings":["University of Rome \"La Sapienza\", Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Rome \"La Sapienza\", Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024394882","display_name":"Andrea Sterbini","orcid":"https://orcid.org/0000-0002-5361-2786"},"institutions":[{"id":"https://openalex.org/I861853513","display_name":"Sapienza University of Rome","ror":"https://ror.org/02be6w209","country_code":"IT","type":"education","lineage":["https://openalex.org/I861853513"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"STERBINI, Andrea","raw_affiliation_strings":["University of Rome \"La Sapienza\", Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Rome \"La Sapienza\", Rome, Italy","institution_ids":["https://openalex.org/I861853513"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5019855296","https://openalex.org/A5024394882"],"corresponding_institution_ids":["https://openalex.org/I39422238","https://openalex.org/I861853513"],"apc_list":null,"apc_paid":null,"fwci":0.98,"has_fulltext":false,"cited_by_count":51,"citation_normalized_percentile":{"value":0.79227381,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":null,"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":0.9998999834060669,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.996999979019165,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.9958999752998352,"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/combinatorics","display_name":"Combinatorics","score":0.8953791260719299},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8023035526275635},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.531875491142273},{"id":"https://openalex.org/keywords/disjoint-sets","display_name":"Disjoint sets","score":0.5246955752372742},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.49536001682281494},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4330795407295227},{"id":"https://openalex.org/keywords/cograph","display_name":"Cograph","score":0.4155942499637604},{"id":"https://openalex.org/keywords/pathwidth","display_name":"Pathwidth","score":0.22304239869117737},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.13953232765197754}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8953791260719299},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8023035526275635},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.531875491142273},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.5246955752372742},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.49536001682281494},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4330795407295227},{"id":"https://openalex.org/C59824394","wikidata":"https://www.wikidata.org/wiki/Q5141281","display_name":"Cograph","level":5,"score":0.4155942499637604},{"id":"https://openalex.org/C43517604","wikidata":"https://www.wikidata.org/wiki/Q7144893","display_name":"Pathwidth","level":4,"score":0.22304239869117737},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.13953232765197754}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:iris.uniroma1.it:11573/245353","is_oa":false,"landing_page_url":"http://hdl.handle.net/11573/245353","pdf_url":null,"source":{"id":"https://openalex.org/S4377196107","display_name":"IRIS Research product catalog (Sapienza University of Rome)","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":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":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":2,"referenced_works":["https://openalex.org/W2000506665","https://openalex.org/W2314893179"],"related_works":["https://openalex.org/W3160792420","https://openalex.org/W4287181997","https://openalex.org/W2886071965","https://openalex.org/W4297803065","https://openalex.org/W3168725788","https://openalex.org/W1553466895","https://openalex.org/W2079856162","https://openalex.org/W1978588354","https://openalex.org/W416686103","https://openalex.org/W2397003135"],"abstract_inverted_index":{"Among":[0],"all":[1],"simple":[2],"graphs":[3],"on":[4,104],"n":[5,61],"vertices":[6],"and":[7,62,79,84,93,97,113,145],"e":[8,63],"edges,":[9],"which":[10],"ones":[11],"have":[12],"the":[13,19,70,126,153],"largest":[14],"sum":[15],"of":[16,18,69,87],"squares":[17],"vertex":[20],"degrees?":[21],"It":[22],"is":[23,38,89],"easy":[24],"to":[25],"see":[26],"that":[27,58,85,148],"they":[28],"must":[29],"be":[30],"threshold":[31,36,123],"graphs,":[32,99],"but":[33],"not":[34],"every":[35,149],"graph":[37,68,124,151],"optimal":[39,150],"in":[40,125],"this":[41],"sense.":[42],"Boesch":[43],"et":[44,47],"al.":[45],"[Boesch":[46],"al.,":[48],"Tech":[49],"Rep,":[50],"Stevens":[51],"Inst":[52],"Tech,":[53],"Hoboken":[54],"NJ,":[55],"1990]":[56],"showed":[57],"for":[59],"given":[60],"there":[64],"exists":[65],"exactly":[66,80],"one":[67,81,86],"form":[71,127,154],"G1(p,q,r)":[72],"=":[73,83,130],"Kp":[74],"+":[75,106,114,132,136],"(Sq":[76],"\u222a":[77,109,134,138],"K1,r)":[78],"G2(p,q,r)":[82],"them":[88],"optimal,":[90],"where":[91],"K":[92],"S":[94],"indicate":[95],"complete":[96,116],"edgeless":[98],"K1,r":[100],"indicates":[101,110,115],"a":[102,121],"star":[103],"r":[105],"1":[107,161,165],"vertices,":[108],"disjoint":[111,117],"union,":[112],"join.":[118],"We":[119],"specify":[120],"general":[122],"G(a,b,c,d,":[128,143],"\u2026)":[129],"Ka":[131],"(Sb":[133],"(Kc":[135],"(Sd":[137],"\u00b7\u00b7\u00b7)))":[139],"or":[140,156,162,166],"its":[141],"complement":[142],"\u2026),":[144],"we":[146],"prove":[147],"has":[152],"G(a,b,c,d)":[155,157],"with":[158],"b":[159],"\u2a7d":[160,164,168],"c":[163],"d":[167],"1.":[169],"\u00a9":[170],"1999":[171,182],"John":[172],"Wiley":[173],"&":[174],"Sons,":[175],"Inc.":[176],"J":[177],"Graph":[178],"Theory":[179],"31:":[180],"283\u2013295,":[181]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2014,"cited_by_count":4},{"year":2013,"cited_by_count":3}],"updated_date":"2026-06-17T08:01:34.144755","created_date":"2025-10-10T00:00:00"}