{"id":"https://openalex.org/W7167020941","doi":"https://doi.org/10.48550/arxiv.2607.00519","title":"A Geometric View of Combinatorial Fiedler Theory","display_name":"A Geometric View of Combinatorial Fiedler Theory","publication_year":2026,"publication_date":"2026-07-01","ids":{"openalex":"https://openalex.org/W7167020941","doi":"https://doi.org/10.48550/arxiv.2607.00519"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2607.00519","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00519","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,"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2607.00519","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5043388541","display_name":"Jos\u00e9 Fern\u00e1ndez Goycoolea","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Goycoolea, Jos\u00e9 Fern\u00e1ndez","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5008516454","display_name":"Andrea de las Heras-Parrilla","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Heras-Parrilla, Andrea de las","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073598233","display_name":"Luis H. Herrera","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Herrera, Luis H.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5032873622","display_name":"Clemens Huemer","orcid":"https://orcid.org/0000-0001-7557-0823"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huemer, Clemens","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136771201","display_name":"Carlos Seara","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Seara, Carlos","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"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":0.6953999996185303,"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":0.6953999996185303,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.07569999992847443,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.07519999891519547,"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/maximization","display_name":"Maximization","score":0.7279000282287598},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.4733999967575073},{"id":"https://openalex.org/keywords/algebraic-connectivity","display_name":"Algebraic connectivity","score":0.4293999969959259},{"id":"https://openalex.org/keywords/quotient","display_name":"Quotient","score":0.4275999963283539},{"id":"https://openalex.org/keywords/degeneracy","display_name":"Degeneracy (biology)","score":0.41519999504089355},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.4002000093460083},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.388700008392334},{"id":"https://openalex.org/keywords/graph-theory","display_name":"Graph theory","score":0.3650999963283539}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7540000081062317},{"id":"https://openalex.org/C2776330181","wikidata":"https://www.wikidata.org/wiki/Q18358244","display_name":"Maximization","level":2,"score":0.7279000282287598},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5655999779701233},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.4733999967575073},{"id":"https://openalex.org/C7948225","wikidata":"https://www.wikidata.org/wiki/Q4723998","display_name":"Algebraic connectivity","level":4,"score":0.4293999969959259},{"id":"https://openalex.org/C199422724","wikidata":"https://www.wikidata.org/wiki/Q41118","display_name":"Quotient","level":2,"score":0.4275999963283539},{"id":"https://openalex.org/C2777727622","wikidata":"https://www.wikidata.org/wiki/Q5251772","display_name":"Degeneracy (biology)","level":2,"score":0.41519999504089355},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.4002000093460083},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.39100000262260437},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.388700008392334},{"id":"https://openalex.org/C88230418","wikidata":"https://www.wikidata.org/wiki/Q131476","display_name":"Graph theory","level":2,"score":0.3650999963283539},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.33410000801086426},{"id":"https://openalex.org/C2778158742","wikidata":"https://www.wikidata.org/wiki/Q1665115","display_name":"Rayleigh quotient","level":3,"score":0.32109999656677246},{"id":"https://openalex.org/C165700671","wikidata":"https://www.wikidata.org/wiki/Q203484","display_name":"Laplace operator","level":2,"score":0.30809998512268066},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.29789999127388},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.28060001134872437},{"id":"https://openalex.org/C103646786","wikidata":"https://www.wikidata.org/wiki/Q5179260","display_name":"Covering problems","level":3,"score":0.27959999442100525},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2784999907016754},{"id":"https://openalex.org/C52692508","wikidata":"https://www.wikidata.org/wiki/Q1333872","display_name":"Combinatorial optimization","level":2,"score":0.2630000114440918},{"id":"https://openalex.org/C115178988","wikidata":"https://www.wikidata.org/wiki/Q772067","display_name":"Laplacian matrix","level":3,"score":0.2590999901294708}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2607.00519","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00519","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,"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":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2607.00519","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2607.00519","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,"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Recently,":[0],"Andrade":[1],"and":[2,88,133,153],"Dahl":[3],"introduced":[4],"combinatorial":[5,83],"Fiedler":[6],"theory":[7],"by":[8,166],"studying":[9],"a":[10,28,65,101,110],"parameter":[11,57],"$b(G)$":[12,152],"defined":[13],"as":[14],"the":[15,18,24,36,42,45,48,55,71,74,86,124,138,146,160,167,175],"$\\ell_1$-analog":[16,46],"of":[17,23,27,44,47,73,79,85,140,148,162],"Rayleigh":[19],"quotient":[20],"minimization":[21,87],"characterization":[22],"algebraic":[25],"connectivity":[26],"graph":[29,157],"$G=(V,E)$.":[30],"In":[31],"this":[32,61,121,179],"work,":[33],"we":[34,144,171],"study":[35],"corresponding":[37],"maximization":[38,62,89],"problem,":[39],"which":[40],"plays":[41],"role":[43],"largest":[49,76,169],"Laplacian":[50],"eigenvalue.":[51],"We":[52],"show":[53],"that":[54,126,173,177],"new":[56],"$B(G)$":[58,154,163],"associated":[59],"with":[60,109],"problem":[63],"admits":[64],"simple":[66],"exact":[67],"description:":[68],"it":[69],"is":[70,91,107,118,164,181],"average":[72],"two":[75,168],"vertex":[77],"degrees":[78],"$G$.":[80],"A":[81],"unified":[82],"treatment":[84],"problems":[90,97],"presented":[92,119],"first.":[93],"Later,":[94],"both":[95],"optimization":[96],"are":[98],"reinterpreted":[99],"in":[100],"geometrical":[102],"setting.":[103],"The":[104],"feasible":[105],"set":[106],"identified":[108],"$(n-2)$-dimensional":[111],"cuboctahedron":[112],"shell":[113],"where":[114],"$n=|V|$.":[115],"Additional":[116],"structure":[117],"for":[120,151,155],"polyhedron,":[122],"including":[123],"fact":[125],"maximizing":[127],"solutions":[128,135],"arise":[129,136],"at":[130,137],"its":[131,141],"vertices":[132],"minimizing":[134],"centers":[139],"facets.":[142],"Finally,":[143],"analyze":[145],"number":[147],"optimal":[149],"vectors":[150,176],"several":[156],"families.":[158],"Although":[159],"value":[161,180],"determined":[165],"degrees,":[170],"prove":[172],"counting":[174],"attain":[178],"actually":[182],"$\\#\\mathrm{P}$-complete.":[183]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-07-03T00:00:00"}
