{"id":"https://openalex.org/W1515697879","doi":"https://doi.org/10.37236/173","title":"Properties Determined by the Ihara Zeta Function of a Graph","display_name":"Properties Determined by the Ihara Zeta Function of a Graph","publication_year":2009,"publication_date":"2009-07-09","ids":{"openalex":"https://openalex.org/W1515697879","doi":"https://doi.org/10.37236/173","mag":"1515697879"},"language":"en","primary_location":{"id":"doi:10.37236/173","is_oa":true,"landing_page_url":"https://doi.org/10.37236/173","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r84/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":null,"license_id":null,"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/v16i1r84/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5051327555","display_name":"Yaim Cooper","orcid":null},"institutions":[{"id":"https://openalex.org/I20089843","display_name":"Princeton University","ror":"https://ror.org/00hx57361","country_code":"US","type":"education","lineage":["https://openalex.org/I20089843"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Yaim Cooper","raw_affiliation_strings":["Department of Mathematics Princeton, NJ, USA","Princeton University#TAB#"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics Princeton, NJ, USA","institution_ids":["https://openalex.org/I20089843"]},{"raw_affiliation_string":"Princeton University#TAB#","institution_ids":["https://openalex.org/I20089843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5051327555"],"corresponding_institution_ids":["https://openalex.org/I20089843"],"apc_list":null,"apc_paid":null,"fwci":1.928,"has_fulltext":true,"cited_by_count":29,"citation_normalized_percentile":{"value":0.83116883,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"16","issue":"1","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":1.0,"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":1.0,"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/T12541","display_name":"Graph Labeling and Dimension Problems","score":0.9952999949455261,"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"}},{"id":"https://openalex.org/T10374","display_name":"Advanced Graph Theory Research","score":0.987500011920929,"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":0.8510892391204834},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8393692970275879},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.5852953791618347},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5663984417915344},{"id":"https://openalex.org/keywords/digraph","display_name":"Digraph","score":0.53508061170578},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5224375128746033},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3851492702960968},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.11373597383499146}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8510892391204834},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8393692970275879},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.5852953791618347},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5663984417915344},{"id":"https://openalex.org/C2779145032","wikidata":"https://www.wikidata.org/wiki/Q191494","display_name":"Digraph","level":2,"score":0.53508061170578},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5224375128746033},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3851492702960968},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.11373597383499146}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/173","is_oa":true,"landing_page_url":"https://doi.org/10.37236/173","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r84/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.214.5160","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.214.5160","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.combinatorics.org/Volume_16/PDF/v16i1r84.pdf","raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/173","is_oa":true,"landing_page_url":"https://doi.org/10.37236/173","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v16i1r84/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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1966406512","display_name":"REU Site in Mathematics at Louisiana State University","funder_award_id":"0353722","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"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1515697879.pdf","grobid_xml":"https://content.openalex.org/works/W1515697879.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W1523808012","https://openalex.org/W2043558432","https://openalex.org/W2142193905","https://openalex.org/W2762804755","https://openalex.org/W4251636534"],"related_works":["https://openalex.org/W2038088825","https://openalex.org/W1975203667","https://openalex.org/W2370328482","https://openalex.org/W2082494488","https://openalex.org/W2998116189","https://openalex.org/W2054349495","https://openalex.org/W2081358954","https://openalex.org/W2019041327","https://openalex.org/W2554461497","https://openalex.org/W2945242988"],"abstract_inverted_index":{"In":[0],"this":[1,171],"paper,":[2],"we":[3,32,46,60,89],"show":[4,33,70,140],"how":[5,34,71],"to":[6,35,72,94,174],"determine":[7,73],"several":[8,96,115],"properties":[9,116],"of":[10,39,41,50,65,92,99,101,117,177],"a":[11,48],"finite":[12],"graph":[13,143],"$G$":[14,22,57,75,144,181],"from":[15,152,185],"its":[16,81,153,186],"Ihara":[17,108,129,161,187],"zeta":[18,109,130,162,188],"function":[19,163],"$Z_{G}(u)$.":[20],"If":[21],"is":[23,58,76],"connected":[24],"and":[25,52,78,83,121],"has":[26],"minimal":[27],"degree":[28],"at":[29],"least":[30],"2,":[31],"calculate":[36],"the":[37,54,86,106,128,159,175],"number":[38],"vertices":[40,148],"$G$.":[42],"To":[43],"do":[44],"so":[45],"use":[47],"result":[49],"Bass,":[51],"in":[53],"case":[55],"that":[56,114,141],"nonbipartite,":[59],"give":[61,95],"an":[62],"elementary":[63],"proof":[64],"Bass'":[66],"result.":[67],"We":[68,132,139],"further":[69],"whether":[74],"regular,":[77],"if":[79],"so,":[80],"regularity":[82],"spectrum.":[84],"On":[85],"other":[87],"hand,":[88],"extend":[90],"work":[91],"Czarneski":[93],"infinite":[97],"families":[98],"pairs":[100],"non-isomorphic":[102],"non-regular":[103],"graphs":[104,157],"with":[105,134,145,158,167],"same":[107,160],"function.":[110,131,189],"These":[111],"examples":[112],"demonstrate":[113],"graphs,":[118],"including":[119],"vertex":[120],"component":[122],"numbers,":[123],"are":[124,164],"not":[125],"determined":[126],"by":[127],"end":[133],"Hashimoto's":[135],"edge":[136],"matrix":[137],"T.":[138],"any":[142],"no":[146],"isolated":[147],"can":[149,182],"be":[150,183],"recovered":[151,184],"$T$":[154],"matrix.":[155],"Since":[156],"exactly":[165],"those":[166],"isospectral":[168],"T":[169],"matrices,":[170],"relates":[172],"again":[173],"question":[176],"what":[178],"information":[179],"about":[180]},"counts_by_year":[{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":3}],"updated_date":"2026-04-10T15:06:20.359241","created_date":"2025-10-10T00:00:00"}