{"id":"https://openalex.org/W3097178077","doi":"https://doi.org/10.37236/9179","title":"The Maximum Spectral Radius of Graphs Without Friendship Subgraphs","display_name":"The Maximum Spectral Radius of Graphs Without Friendship Subgraphs","publication_year":2020,"publication_date":"2020-10-30","ids":{"openalex":"https://openalex.org/W3097178077","doi":"https://doi.org/10.37236/9179","mag":"3097178077"},"language":"en","primary_location":{"id":"doi:10.37236/9179","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9179","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p22/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/v27i4p22/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5002085058","display_name":"Sebastian M. Cioab\u0103","orcid":"https://orcid.org/0000-0001-9983-0212"},"institutions":[{"id":"https://openalex.org/I86501945","display_name":"University of Delaware","ror":"https://ror.org/01sbq1a82","country_code":"US","type":"education","lineage":["https://openalex.org/I86501945"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Sebastian Cioab\u0103","raw_affiliation_strings":["University of Delaware"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Delaware","institution_ids":["https://openalex.org/I86501945"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060317661","display_name":"Lihua Feng","orcid":"https://orcid.org/0000-0003-4144-1649"},"institutions":[{"id":"https://openalex.org/I139660479","display_name":"Central South University","ror":"https://ror.org/00f1zfq44","country_code":"CN","type":"education","lineage":["https://openalex.org/I139660479"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lihua Feng","raw_affiliation_strings":["Central South University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Central South University","institution_ids":["https://openalex.org/I139660479"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5054251227","display_name":"Michael Tait","orcid":"https://orcid.org/0000-0003-3695-6883"},"institutions":[{"id":"https://openalex.org/I7863295","display_name":"Villanova University","ror":"https://ror.org/02g7kd627","country_code":"US","type":"education","lineage":["https://openalex.org/I7863295"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Michael Tait","raw_affiliation_strings":["Villanova University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Villanova University","institution_ids":["https://openalex.org/I7863295"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5100376227","display_name":"Xiao\u2010Dong Zhang","orcid":"https://orcid.org/0000-0003-0783-051X"},"institutions":[{"id":"https://openalex.org/I183067930","display_name":"Shanghai Jiao Tong University","ror":"https://ror.org/0220qvk04","country_code":"CN","type":"education","lineage":["https://openalex.org/I183067930"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao-Dong Zhang","raw_affiliation_strings":["Shanghai Jiao Tong University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai Jiao Tong University","institution_ids":["https://openalex.org/I183067930"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":12.3905,"has_fulltext":true,"cited_by_count":76,"citation_normalized_percentile":{"value":0.99380805,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"27","issue":"4","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9991000294685364,"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/T11797","display_name":"graph theory and CDMA systems","score":0.960099995136261,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.9398999810218811,"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":0.8562543392181396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7909748554229736},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.78697669506073},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6741619110107422},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.6194013357162476},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5397136807441711},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4118233323097229},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.12134918570518494},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08886006474494934},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.040525734424591064}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8562543392181396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7909748554229736},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.78697669506073},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6741619110107422},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.6194013357162476},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5397136807441711},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4118233323097229},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.12134918570518494},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08886006474494934},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.040525734424591064}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/9179","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9179","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p22/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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:10.37236/9179","is_oa":true,"landing_page_url":"https://doi.org/10.37236/9179","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v27i4p22/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[{"display_name":"Reduced inequalities","id":"https://metadata.un.org/sdg/10","score":0.44999998807907104}],"awards":[{"id":"https://openalex.org/G1356089975","display_name":null,"funder_award_id":"2016JJ2138, 2018JJ2479","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G2120803139","display_name":null,"funder_award_id":"2011553","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G2594570067","display_name":"\u6781\u503c\u4e0e\u4ee3\u6570\u56fe\u8bba\u4e2d\u7684\u7279\u5f81\u503c\u95ee\u9898\u7684\u7814\u7a76","funder_award_id":"11871479","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3570350311","display_name":null,"funder_award_id":"CIF-1815922","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3581516001","display_name":null,"funder_award_id":"11671402","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G4360425028","display_name":"ANALYSIS OF NEUROLOGICAL DISORDERS USING THREE DIMENSIONAL SPIRAL SCAN FUNCTIONAL BRAIN MAPPING","funder_award_id":"11671402","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"},{"id":"https://openalex.org/G5242831038","display_name":null,"funder_award_id":"2016JJ2138","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G568667519","display_name":"The Interplay between Spectral and Combinatorial Properties of Graphs and Association Schemes","funder_award_id":"1600768","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6323940620","display_name":null,"funder_award_id":"DMS-2011553","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G6431929763","display_name":null,"funder_award_id":"2016JJ2138","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G6697670454","display_name":null,"funder_award_id":"2018JJ2479","funder_id":"https://openalex.org/F4320322843","funder_display_name":"Natural Science Foundation of\u00a0Hunan Province"},{"id":"https://openalex.org/G7270993960","display_name":null,"funder_award_id":"DMS-1600768","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G736147581","display_name":null,"funder_award_id":"11971311","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G7436681347","display_name":"\u4ee3\u6570\u7ed3\u6784\u7684\u5173\u8054\u56fe\u7684\u81ea\u540c\u6784\u7fa4\u53ca\u5176\u56fe\u8bba\u6027\u8d28\u7814\u7a76","funder_award_id":"11671402","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8381071902","display_name":null,"funder_award_id":"11531001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8850655570","display_name":null,"funder_award_id":"2018JJ2479","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8963788510","display_name":"Analytic and Geometric Inverse Problems and Related Topics","funder_award_id":"1815922","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322843","display_name":"Natural Science Foundation of\u00a0Hunan Province","ror":null},{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3097178077.pdf","grobid_xml":"https://content.openalex.org/works/W3097178077.grobid-xml"},"referenced_works_count":24,"referenced_works":["https://openalex.org/W1676972809","https://openalex.org/W1967121281","https://openalex.org/W1977170634","https://openalex.org/W1984835757","https://openalex.org/W2018421682","https://openalex.org/W2020049876","https://openalex.org/W2078483670","https://openalex.org/W2080890097","https://openalex.org/W2083580384","https://openalex.org/W2087749018","https://openalex.org/W2087818660","https://openalex.org/W2093276208","https://openalex.org/W2112658668","https://openalex.org/W2120651585","https://openalex.org/W2121529848","https://openalex.org/W2123435414","https://openalex.org/W2148664602","https://openalex.org/W2155085924","https://openalex.org/W2164542539","https://openalex.org/W2963003173","https://openalex.org/W2963490393","https://openalex.org/W4213084269","https://openalex.org/W6648525765","https://openalex.org/W6654950072"],"related_works":["https://openalex.org/W2611163850","https://openalex.org/W83388600","https://openalex.org/W2962954592","https://openalex.org/W1845849701","https://openalex.org/W2982430984","https://openalex.org/W1989875658","https://openalex.org/W4293788411","https://openalex.org/W2962951545","https://openalex.org/W2900798793","https://openalex.org/W4301046126"],"abstract_inverted_index":{"A":[0],"graph":[1,20],"on":[2],"$2k+1$":[3],"vertices":[4],"consisting":[5],"of":[6,30],"$k$":[7],"triangles":[8],"which":[9],"intersect":[10],"in":[11],"exactly":[12],"one":[13],"common":[14],"vertex":[15],"is":[16],"called":[17],"a":[18],"$k-$friendship":[19],"and":[21],"denoted":[22],"by":[23],"$F_k$.":[24],"This":[25],"paper":[26],"determines":[27],"the":[28,35],"graphs":[29,42],"order":[31],"$n$":[32,47],"that":[33],"have":[34],"maximum":[36],"(adjacency)":[37],"spectral":[38],"radius":[39],"among":[40],"all":[41],"containing":[43],"no":[44],"$F_k$,":[45],"for":[46],"sufficiently":[48],"large.":[49]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":18},{"year":2024,"cited_by_count":23},{"year":2023,"cited_by_count":11},{"year":2022,"cited_by_count":12},{"year":2021,"cited_by_count":9}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
