{"id":"https://openalex.org/W7213429954","doi":"https://doi.org/10.48550/arxiv.2609.16049","title":"An endpoint exception to a conjectured equality characterization for Laplacian eigenvalue products","display_name":"An endpoint exception to a conjectured equality characterization for Laplacian eigenvalue products","publication_year":2026,"publication_date":"2026-09-12","ids":{"openalex":"https://openalex.org/W7213429954","doi":"https://doi.org/10.48550/arxiv.2609.16049"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.16049","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16049","pdf_url":"https://arxiv.org/pdf/2609.16049","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/2609.16049","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5151878581","display_name":"Scott Gibson","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Gibson, Scott","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5151878581"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":2,"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":0.9771000146865845,"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":0.9771000146865845,"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":0.013500000350177288,"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":0.0010000000474974513,"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/laplacian-eigenvalues","display_name":"Laplacian eigenvalues","score":0.9490000009536743},{"id":"https://openalex.org/keywords/counterexample","display_name":"counterexample","score":0.8740000128746033},{"id":"https://openalex.org/keywords/graph-complement","display_name":"graph complement","score":0.6919999718666077},{"id":"https://openalex.org/keywords/connected-graphs","display_name":"connected graphs","score":0.5059999823570251},{"id":"https://openalex.org/keywords/infinite-families-of-graphs","display_name":"infinite families of graphs","score":0.6290000081062317}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.784600019454956},{"id":"https://openalex.org/C162838799","wikidata":"https://www.wikidata.org/wiki/Q596077","display_name":"Counterexample","level":2,"score":0.781499981880188},{"id":"https://openalex.org/C2780841128","wikidata":"https://www.wikidata.org/wiki/Q5073781","display_name":"Characterization (materials science)","level":2,"score":0.7006999850273132},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.6665999889373779},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.6327999830245972},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.5120999813079834},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4521999955177307},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.445499986410141},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.41679999232292175},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.3856000006198883},{"id":"https://openalex.org/C45555294","wikidata":"https://www.wikidata.org/wiki/Q28113351","display_name":"Inequality","level":2,"score":0.3756999969482422},{"id":"https://openalex.org/C39847760","wikidata":"https://www.wikidata.org/wiki/Q1385465","display_name":"Extreme point","level":2,"score":0.3596000075340271},{"id":"https://openalex.org/C63548660","wikidata":"https://www.wikidata.org/wiki/Q858223","display_name":"Limit point","level":2,"score":0.3531999886035919},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3418999910354614},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.3361000120639801},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C154399039","wikidata":"https://www.wikidata.org/wiki/Q1780921","display_name":"Orthogonal complement","level":3,"score":0.2660999894142151},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.2547000050544739}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.16049","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16049","pdf_url":"https://arxiv.org/pdf/2609.16049","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.2609.16049","doi":"https://doi.org/10.48550/arxiv.2609.16049","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.16049","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.16049","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.16049","pdf_url":"https://arxiv.org/pdf/2609.16049","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":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7213429954.pdf","grobid_xml":"https://content.openalex.org/works/W7213429954.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4415819079","https://openalex.org/W7210276463","https://openalex.org/W7169828382","https://openalex.org/W2403450736","https://openalex.org/W7167792935","https://openalex.org/W2891555929","https://openalex.org/W2065676743","https://openalex.org/W3216211874","https://openalex.org/W4308170272","https://openalex.org/W4403846187"],"abstract_inverted_index":{"We":[0],"give":[1],"eight-vertex":[2],"counterexamples":[3],"to":[4,33],"the":[5,27,42,54],"equality":[6],"characterization":[7],"in":[8,57],"Conjecture":[9],"20":[10],"of":[11],"Chen,":[12],"Guo,":[13],"Li":[14],"and":[15,31,44],"Wang,":[16],"Electron.":[17],"J.":[18],"Combin.":[19],"32(4)":[20],"(2025),":[21],"P4.37.":[22],"The":[23],"examples":[24,50],"occur":[25],"at":[26],"included":[28],"endpoint":[29],"$k=3n/4$":[30],"extend":[32],"infinite":[34],"families,":[35],"including":[36],"a":[37],"family":[38],"for":[39],"which":[40],"both":[41],"graph":[43],"its":[45],"complement":[46],"are":[47],"connected.":[48],"These":[49],"do":[51],"not":[52],"contradict":[53],"numerical":[55],"inequality":[56],"that":[58],"conjecture.":[59]},"counts_by_year":[{"year":2026,"cited_by_count":2}],"updated_date":"2026-11-05T12:25:35.769452","created_date":"2026-09-17T00:00:00"}
