{"id":"https://openalex.org/W7213324004","doi":"https://doi.org/10.48550/arxiv.2609.13666","title":"The edge spectral extremal problem for odd wheels in nonzero residue classes","display_name":"The edge spectral extremal problem for odd wheels in nonzero residue classes","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213324004","doi":"https://doi.org/10.48550/arxiv.2609.13666"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.13666","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13666","pdf_url":"https://arxiv.org/pdf/2609.13666","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.13666","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5133166304","display_name":"Honghao Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chen, Honghao","raw_affiliation_strings":["School of Mathematics and Statistics, and Hubei Key Lab-Math. Sci. , Central China Normal University , Wuhan 430079 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, and Hubei Key Lab-Math. Sci. , Central China Normal University , Wuhan 430079 , China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5151738692","display_name":"Jing Gao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gao, Jing","raw_affiliation_strings":["School of Mathematics and Statistics, and Hubei Key Lab-Math. Sci. , Central China Normal University , Wuhan 430079 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, and Hubei Key Lab-Math. Sci. , Central China Normal University , Wuhan 430079 , China","institution_ids":["https://openalex.org/I40963666"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5050604078","display_name":"Shuchao Li","orcid":"https://orcid.org/0000-0002-6856-0827","observed_orcids":["https://orcid.org/0000-0002-6856-0827"]},"institutions":[{"id":"https://openalex.org/I40963666","display_name":"Central China Normal University","ror":"https://ror.org/03x1jna21","country_code":"CN","type":"education","lineage":["https://openalex.org/I40963666"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Li, Shuchao","raw_affiliation_strings":["School of Mathematics and Statistics, and Hubei Key Lab-Math. Sci. , Central China Normal University , Wuhan 430079 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematics and Statistics, and Hubei Key Lab-Math. Sci. , Central China Normal University , Wuhan 430079 , China","institution_ids":["https://openalex.org/I40963666"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I40963666"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"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/T11476","display_name":"Graph theory and applications","score":0.9976000189781189,"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"}},"topics":[{"id":"https://openalex.org/T11476","display_name":"Graph theory and applications","score":0.9976000189781189,"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"}},{"id":"https://openalex.org/T11329","display_name":"Limits and Structures in Graph Theory","score":0.0006000000284984708,"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"}},{"id":"https://openalex.org/T11022","display_name":"Spectral Theory in Mathematical Physics","score":0.00019999999494757503,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/extremal-graph-theory","display_name":"extremal graph theory","score":0.7720000147819519},{"id":"https://openalex.org/keywords/extremal-graphs","display_name":"extremal graphs","score":0.47200000286102295}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8309000134468079},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.7930999994277954},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.7229999899864197},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5375999808311462},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5011000037193298},{"id":"https://openalex.org/C110484373","wikidata":"https://www.wikidata.org/wiki/Q264398","display_name":"Adjacency list","level":2,"score":0.499099999666214},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4925999939441681},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.41510000824928284},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.3874000012874603},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3271999955177307},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C180356752","wikidata":"https://www.wikidata.org/wiki/Q727035","display_name":"Adjacency matrix","level":3,"score":0.30300000309944153},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C169827030","wikidata":"https://www.wikidata.org/wiki/Q2294516","display_name":"Dual graph","level":4,"score":0.27889999747276306},{"id":"https://openalex.org/C2985906921","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Spectral properties","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C181888306","wikidata":"https://www.wikidata.org/wiki/Q6535097","display_name":"Level structure","level":3,"score":0.26429998874664307},{"id":"https://openalex.org/C76444178","wikidata":"https://www.wikidata.org/wiki/Q72897900","display_name":"Connectivity","level":3,"score":0.2612000107765198}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.13666","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13666","pdf_url":"https://arxiv.org/pdf/2609.13666","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},{"id":"doi:10.48550/arxiv.2609.13666","doi":"https://doi.org/10.48550/arxiv.2609.13666","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.13666","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.13666","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.13666","pdf_url":"https://arxiv.org/pdf/2609.13666","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"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":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G3399293828","display_name":null,"funder_award_id":"12171190","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G3552376439","display_name":null,"funder_award_id":"12571365","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213324004.pdf","grobid_xml":"https://content.openalex.org/works/W7213324004.grobid-xml"},"referenced_works_count":4,"referenced_works":["https://openalex.org/W4409509054","https://openalex.org/W4416050753","https://openalex.org/W7201856547","https://openalex.org/W7203710947"],"related_works":["https://openalex.org/W7214360594","https://openalex.org/W7203710947","https://openalex.org/W3153244529","https://openalex.org/W4409509054","https://openalex.org/W4406902487","https://openalex.org/W6955562783","https://openalex.org/W7220905976","https://openalex.org/W4310437424","https://openalex.org/W3131702536","https://openalex.org/W4417343656"],"abstract_inverted_index":{"For":[0,51],"a":[1,120,154],"fixed":[2],"integer":[3],"$k\\ge":[4,86,187],"2$,":[5],"let":[6],"$W_{2k+1}=K_1\\vee":[7],"C_{2k}$":[8],"be":[9,119],"an":[10],"odd":[11],"wheel":[12],"graph.":[13],"The":[14],"fixed-size":[15],"spectral":[16,36,143],"extremal":[17],"problem":[18,101,173],"aims":[19],"to":[20,160],"determine":[21],"\\[":[22],"\\operatorname{spex}(m,W_{2k+1}):=\\max\\{\u03c1(G):":[23],"e(G)=m,\\":[24],"G":[25],"\\text{":[26],"is":[27,84,90,102,125,131,147],"}":[28],"W_{2k+1}\\text{-free}\\},":[29],"\\]":[30],"where":[31,145],"$\u03c1(G)$":[32],"denotes":[33],"the":[34,48,79,95,99,114,132,165,183],"adjacency":[35],"radius.":[37],"Based":[38],"on":[39],"this":[40,106,168,172],"problem,":[41,107],"Yu,":[42,108],"Li,":[43],"and":[44,69,75,88,110,157],"Peng":[45],"[18]":[46],"proposed":[47,113],"following":[49,115],"conjecture:":[50,116],"large":[52],"$m$,":[53],"every":[54],"$W_{2k+1}$-free":[55,136],"graph":[56,134],"of":[57,138,164],"size":[58,139],"$m$":[59,83,140],"satisfies":[60],"$\u03c1(G)^2-(k-1)\u03c1(G)\\le":[61],"m-\\binom{k}{2}$":[62],"with":[63],"equality":[64],"precisely":[65],"for":[66,98,186],"$K_k\\vee":[67,150],"qK_1$":[68,151],"$m-\\binom{k}{2}=kq$.":[70],"Very":[71],"recently,":[72],"Fang,":[73],"Zhai":[74],"Zhang":[76,111],"[7]":[77],"confirmed":[78],"Yu--Li--Peng":[80],"conjecture.":[81],"When":[82],"large,":[85],"2$":[87],"$m-\\binom{k}{2}$":[89,124],"not":[91],"divisible":[92],"by":[93,127,152],"$k$,":[94],"exact":[96],"solution":[97],"above":[100],"still":[103],"open.":[104],"Regarding":[105],"Zhang,":[109],"[19]":[112],"Let":[117],"$r$":[118,162],"nonzero":[121,176],"remainder":[122],"when":[123],"divided":[126],"$k$.":[128],"Then":[129],"$S_{k,m}$":[130,146],"unique":[133],"among":[135],"graphs":[137],"having":[141],"maximum":[142],"radius,":[144],"obtained":[148],"from":[149],"adding":[153],"vertex":[155],"$z$":[156],"joining":[158],"it":[159],"exactly":[161],"vertices":[163],"$K_k$.":[166],"In":[167],"paper":[169],"we":[170],"address":[171],"in":[174],"each":[175],"residue":[177],"class.":[178],"Our":[179],"result":[180],"completely":[181],"settles":[182],"Yu-Zhang-Zhang":[184],"conjecture":[185],"3$.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":3}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-09-16T00:00:00"}
