{"id":"https://openalex.org/W7163715459","doi":"https://doi.org/10.37236/14952","title":"The $\\alpha$-Spectral Tur\u00e1n Type Problems for Graphs","display_name":"The $\\alpha$-Spectral Tur\u00e1n Type Problems for Graphs","publication_year":2026,"publication_date":"2026-06-05","ids":{"openalex":"https://openalex.org/W7163715459","doi":"https://doi.org/10.37236/14952"},"language":null,"primary_location":{"id":"doi:10.37236/14952","is_oa":true,"landing_page_url":"https://doi.org/10.37236/14952","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p48/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/v33i2p48/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137988723","display_name":"Jiadong Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiadong Wu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101354530","display_name":"Yongchun Lu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yongchun Lu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137947177","display_name":"Liying Kang","orcid":null},"institutions":[{"id":"https://openalex.org/I113940042","display_name":"Shanghai University","ror":"https://ror.org/006teas31","country_code":"CN","type":"education","lineage":["https://openalex.org/I113940042"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liying Kang","raw_affiliation_strings":["Shanghai University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Shanghai University","institution_ids":["https://openalex.org/I113940042"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.79297057,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"2","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":0.8878999948501587,"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":0.8878999948501587,"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/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.04960000142455101,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.012500000186264515,"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/adjacency-matrix","display_name":"Adjacency matrix","score":0.679099977016449},{"id":"https://openalex.org/keywords/spectral-radius","display_name":"Spectral radius","score":0.6560999751091003},{"id":"https://openalex.org/keywords/eigenvalues-and-eigenvectors","display_name":"Eigenvalues and eigenvectors","score":0.5489000082015991},{"id":"https://openalex.org/keywords/laplacian-matrix","display_name":"Laplacian matrix","score":0.5404000282287598},{"id":"https://openalex.org/keywords/diagonal-matrix","display_name":"Diagonal matrix","score":0.5389999747276306},{"id":"https://openalex.org/keywords/adjacency-list","display_name":"Adjacency list","score":0.46059998869895935},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.454800009727478},{"id":"https://openalex.org/keywords/diagonal","display_name":"Diagonal","score":0.40790000557899475}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7603999972343445},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7519000172615051},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.679099977016449},{"id":"https://openalex.org/C140532419","wikidata":"https://www.wikidata.org/wiki/Q249748","display_name":"Spectral radius","level":3,"score":0.6560999751091003},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5489000082015991},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.5404000282287598},{"id":"https://openalex.org/C113313756","wikidata":"https://www.wikidata.org/wiki/Q332791","display_name":"Diagonal matrix","level":3,"score":0.5389999747276306},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.5184000134468079},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.46059998869895935},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.454800009727478},{"id":"https://openalex.org/C130367717","wikidata":"https://www.wikidata.org/wiki/Q189791","display_name":"Diagonal","level":2,"score":0.40790000557899475},{"id":"https://openalex.org/C196956537","wikidata":"https://www.wikidata.org/wiki/Q202021","display_name":"Chromatic scale","level":2,"score":0.4049000144004822},{"id":"https://openalex.org/C78913703","wikidata":"https://www.wikidata.org/wiki/Q5597087","display_name":"Graph energy","level":5,"score":0.3262999951839447},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3237999975681305},{"id":"https://openalex.org/C2985491264","wikidata":"https://www.wikidata.org/wiki/Q761631","display_name":"Clique number","level":3,"score":0.3212999999523163},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.31290000677108765},{"id":"https://openalex.org/C70488441","wikidata":"https://www.wikidata.org/wiki/Q5504427","display_name":"Friendship graph","level":5,"score":0.30559998750686646},{"id":"https://openalex.org/C2779773260","wikidata":"https://www.wikidata.org/wiki/Q11246292","display_name":"Signed graph","level":3,"score":0.2921999990940094},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C74003402","wikidata":"https://www.wikidata.org/wiki/Q3180727","display_name":"Spectral graph theory","level":5,"score":0.2865000069141388},{"id":"https://openalex.org/C162199024","wikidata":"https://www.wikidata.org/wiki/Q3085391","display_name":"Degree matrix","level":5,"score":0.28299999237060547},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.27970001101493835},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.2624000012874603}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.37236/14952","is_oa":true,"landing_page_url":"https://doi.org/10.37236/14952","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p48/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:10.37236/14952","is_oa":true,"landing_page_url":"https://doi.org/10.37236/14952","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v33i2p48/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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7163715459.pdf","grobid_xml":"https://content.openalex.org/works/W7163715459.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"For":[0],"$0":[1],"\\leq":[2],"\\alpha":[3],"&lt;":[4],"1$,":[5],"the":[6,16,27,65,76,93,101,107,116],"$\\alpha$-spectral":[7,94,108],"radius":[8],"of":[9,19,30,35,68,84,96],"a":[10],"graph":[11,39],"$G$":[12],"is":[13,40,64],"defined":[14],"as":[15],"largest":[17],"eigenvalue":[18],"$A_{\\alpha}(G)=\\alpha":[20],"D(G)+(1-\\alpha)A(G)$,":[21],"where":[22,62],"$D(G)$":[23],"and":[24,32,71,79,122],"$A(G)$":[25],"are":[26],"diagonal":[28],"matrix":[29,34],"degrees":[31],"adjacency":[33,77,120],"$G$,":[36],"respectively.":[37,87],"A":[38],"called":[41],"color-critical":[42,112],"if":[43],"it":[44],"contains":[45],"an":[46],"edge":[47],"whose":[48],"deletion":[49],"reduces":[50],"its":[51],"chromatic":[52,66],"number.":[53],"The":[54],"celebrated":[55],"Erd\\H{o}s-Stone-Simonovits":[56],"theorem":[57],"asserts":[58],"that":[59],"$":[60],"\\mathrm{ex}(n,\\mathcal{F})=\\left(1-\\frac{1}{\\chi(\\mathcal{F})-1}+o(1)\\right)\\frac{n^2}{2},$":[61],"$\\chi(\\mathcal{F})$":[63],"number":[67],"$\\mathcal{F}$.":[69],"Nikiforov":[70],"Zheng":[72],"et":[73],"al.":[74],"established":[75],"spectral":[78,82,121,125],"signless":[80,123],"Laplacian":[81,124],"versions":[83],"this":[85,89,97],"theorem,":[86,98],"In":[88],"paper,":[90],"we":[91,105],"present":[92],"version":[95],"which":[99],"unifies":[100],"aforementioned":[102],"results.":[103],"Furthermore,":[104],"characterize":[106],"extremal":[109,126],"graphs":[110,127],"for":[111,128],"graphs,":[113],"thereby":[114],"extending":[115],"existing":[117],"results":[118],"on":[119],"such":[129],"graphs.":[130]},"counts_by_year":[],"updated_date":"2026-06-07T06:13:29.825681","created_date":"2026-06-06T00:00:00"}
