{"id":"https://openalex.org/W2133973319","doi":"https://doi.org/10.37236/1651","title":"Toida's Conjecture is True","display_name":"Toida's Conjecture is True","publication_year":2002,"publication_date":"2002-03-31","ids":{"openalex":"https://openalex.org/W2133973319","doi":"https://doi.org/10.37236/1651","mag":"2133973319"},"language":"en","primary_location":{"id":"doi:10.37236/1651","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1651","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r35/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":false,"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":"bronze","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r35/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5054526171","display_name":"Edward Dobson","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Edward Dobson","raw_affiliation_strings":["Department of Mathematics and Statistics PO Drawer MA Mississippi State, MS 39762, U.S.A"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Statistics PO Drawer MA Mississippi State, MS 39762, U.S.A","institution_ids":[]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009892196","display_name":"Joy Morris","orcid":"https://orcid.org/0000-0003-2416-669X"},"institutions":[{"id":"https://openalex.org/I107949126","display_name":"University of Lethbridge","ror":"https://ror.org/044j76961","country_code":"CA","type":"education","lineage":["https://openalex.org/I107949126"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"Joy Morris","raw_affiliation_strings":["Department of Mathematics and Computer Science University of Lethbridge Lethbridge, Alberta Canada T1K 3M4"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Computer Science University of Lethbridge Lethbridge, Alberta Canada T1K 3M4","institution_ids":["https://openalex.org/I107949126"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5054526171"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5839,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.6575939,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"9","issue":"1","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998000264167786,"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/T10849","display_name":"Finite Group Theory Research","score":0.9998000264167786,"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/T11797","display_name":"graph theory and CDMA systems","score":0.9902999997138977,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11130","display_name":"Coding theory and cryptography","score":0.9865999817848206,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"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/mathematics","display_name":"Mathematics","score":0.8872653245925903},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8635611534118652},{"id":"https://openalex.org/keywords/conjecture","display_name":"Conjecture","score":0.8515315055847168},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.611858606338501},{"id":"https://openalex.org/keywords/circulant-graph","display_name":"Circulant graph","score":0.5476587414741516},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.5135155320167542},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.46869373321533203},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.45052841305732727},{"id":"https://openalex.org/keywords/automorphism-group","display_name":"Automorphism group","score":0.4478515088558197},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.446095734834671},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4248616695404053},{"id":"https://openalex.org/keywords/voltage-graph","display_name":"Voltage graph","score":0.1216937005519867},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.08405745029449463}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8872653245925903},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8635611534118652},{"id":"https://openalex.org/C2780990831","wikidata":"https://www.wikidata.org/wiki/Q319141","display_name":"Conjecture","level":2,"score":0.8515315055847168},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.611858606338501},{"id":"https://openalex.org/C82190004","wikidata":"https://www.wikidata.org/wiki/Q5121633","display_name":"Circulant graph","level":5,"score":0.5476587414741516},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.5135155320167542},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.46869373321533203},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.45052841305732727},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.4478515088558197},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.446095734834671},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4248616695404053},{"id":"https://openalex.org/C22149727","wikidata":"https://www.wikidata.org/wiki/Q7940747","display_name":"Voltage graph","level":4,"score":0.1216937005519867},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.08405745029449463},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.37236/1651","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1651","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r35/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":false,"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:10.1.1.87.4400","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.87.4400","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uleth.ca/~morris/Research/Toida.pdf","raw_type":"text"},{"id":"pmh:oai:www.uleth.ca:10133/5156","is_oa":false,"landing_page_url":"http://hdl.handle.net/10133/5156","pdf_url":null,"source":{"id":"https://openalex.org/S4306401508","display_name":"Open ULeth Scholarship (OPUS) (University of Lethbridge)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I107949126","host_organization_name":"University of Lethbridge","host_organization_lineage":["https://openalex.org/I107949126"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":{"id":"doi:10.37236/1651","is_oa":true,"landing_page_url":"https://doi.org/10.37236/1651","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v9i1r35/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":false,"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":[],"funders":[{"id":"https://openalex.org/F4320309482","display_name":"Oklahoma State University","ror":"https://ror.org/045ntgf29"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2133973319.pdf","grobid_xml":"https://content.openalex.org/works/W2133973319.grobid-xml"},"referenced_works_count":20,"referenced_works":["https://openalex.org/W1484040084","https://openalex.org/W1967950301","https://openalex.org/W2013737355","https://openalex.org/W2027284944","https://openalex.org/W2029981401","https://openalex.org/W2031171110","https://openalex.org/W2046269186","https://openalex.org/W2051170661","https://openalex.org/W2072678820","https://openalex.org/W2082206348","https://openalex.org/W2094583082","https://openalex.org/W2141456319","https://openalex.org/W2153525410","https://openalex.org/W2333105300","https://openalex.org/W2577139425","https://openalex.org/W2917893419","https://openalex.org/W2970789867","https://openalex.org/W4236779693","https://openalex.org/W4300303686","https://openalex.org/W6607082036"],"related_works":["https://openalex.org/W4378765291","https://openalex.org/W2349424204","https://openalex.org/W2116405749","https://openalex.org/W2962912586","https://openalex.org/W4285120246","https://openalex.org/W2731804756","https://openalex.org/W2884647475","https://openalex.org/W2003567067","https://openalex.org/W2121700246","https://openalex.org/W2098684733"],"abstract_inverted_index":{"Let":[0,11],"$S$":[1],"be":[2,13],"a":[3,14,66,91],"subset":[4],"of":[5,17,23,48,69,93],"the":[6],"units":[7],"in":[8],"${\\bf":[9,24,70],"Z_n}$.":[10],"${\\Gamma}$":[12,52],"circulant":[15,46],"graph":[16,22,47],"order":[18,49],"$n$":[19],"(a":[20],"Cayley":[21],"Z_n}$)":[25],"such":[26],"that":[27,41,77,85],"if":[28,42,58,61],"$ij\\in":[29],"E({\\Gamma})$,":[30],"then":[31,51],"$i":[32],"-":[33],"j$":[34],"(mod":[35],"$n$)":[36],"$\\in":[37],"S$.":[38],"Toida":[39],"conjectured":[40],"$\\Gamma'$":[43],"is":[44,80],"another":[45],"$n$,":[50],"and":[53,59],"${\\Gamma":[54],"'}$":[55],"are":[56,63],"isomorphic":[57,64],"only":[60],"they":[62],"by":[65],"group":[67],"automorphism":[68],"Z_n}$":[71],"In":[72],"this":[73],"paper,":[74],"we":[75],"prove":[76,84],"Toida's":[78,86,94],"conjecture":[79,87],"true.":[81],"We":[82],"further":[83],"implies":[88],"Zibin's":[89],"conjecture,":[90],"generalization":[92],"conjecture.":[95]},"counts_by_year":[{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2017,"cited_by_count":1},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2026-04-05T17:49:38.594831","created_date":"2025-10-10T00:00:00"}
