{"id":"https://openalex.org/W2782514139","doi":"https://doi.org/10.37236/7588","title":"On Certain Edge-Transitive Bicirculants","display_name":"On Certain Edge-Transitive Bicirculants","publication_year":2019,"publication_date":"2019-04-05","ids":{"openalex":"https://openalex.org/W2782514139","doi":"https://doi.org/10.37236/7588","mag":"2782514139"},"language":"en","primary_location":{"id":"doi:10.37236/7588","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7588","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p6/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p6/pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Robert Jajcay","orcid":null},"institutions":[{"id":"https://openalex.org/I74788687","display_name":"Comenius University Bratislava","ror":"https://ror.org/0587ef340","country_code":"SK","type":"education","lineage":["https://openalex.org/I74788687"]}],"countries":["SK"],"is_corresponding":true,"raw_author_name":"Robert Jajcay","raw_affiliation_strings":["Comenius University"],"affiliations":[{"raw_affiliation_string":"Comenius University","institution_ids":["https://openalex.org/I74788687"]}]},{"author_position":"middle","author":{"id":null,"display_name":"\u0160tefko Miklavi\u010d","orcid":null},"institutions":[{"id":"https://openalex.org/I118905719","display_name":"University of Primorska","ror":"https://ror.org/05xefg082","country_code":"SI","type":"education","lineage":["https://openalex.org/I118905719"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"\u0160tefko Miklavi\u010d","raw_affiliation_strings":["University of Primorska"],"affiliations":[{"raw_affiliation_string":"University of Primorska","institution_ids":["https://openalex.org/I118905719"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Primo\u017e \u0160parl","orcid":null},"institutions":[{"id":"https://openalex.org/I153976015","display_name":"University of Ljubljana","ror":"https://ror.org/05njb9z20","country_code":"SI","type":"education","lineage":["https://openalex.org/I153976015"]}],"countries":["SI"],"is_corresponding":false,"raw_author_name":"Primo\u017e \u0160parl","raw_affiliation_strings":["University of Ljubljana"],"affiliations":[{"raw_affiliation_string":"University of Ljubljana","institution_ids":["https://openalex.org/I153976015"]}]},{"author_position":"last","author":{"id":null,"display_name":"Gorazd Vasiljevi\u0107","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gorazd Vasiljevi\u0107","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I74788687"],"apc_list":null,"apc_paid":null,"fwci":3.5475,"has_fulltext":true,"cited_by_count":8,"citation_normalized_percentile":{"value":0.91860836,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"26","issue":"2","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":0.9253000020980835,"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":0.9253000020980835,"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/T11703","display_name":"Rings, Modules, and Algebras","score":0.021700000390410423,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11567","display_name":"semigroups and automata theory","score":0.00559999980032444,"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/automorphism-group","display_name":"Automorphism group","score":0.5227000117301941},{"id":"https://openalex.org/keywords/automorphism","display_name":"Automorphism","score":0.483599990606308},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4510999917984009},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.36890000104904175},{"id":"https://openalex.org/keywords/valence","display_name":"Valence (chemistry)","score":0.3517000079154968}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7893999814987183},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.6294999718666077},{"id":"https://openalex.org/C2988750069","wikidata":"https://www.wikidata.org/wiki/Q60790315","display_name":"Automorphism group","level":3,"score":0.5227000117301941},{"id":"https://openalex.org/C118712358","wikidata":"https://www.wikidata.org/wiki/Q782566","display_name":"Automorphism","level":2,"score":0.483599990606308},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4620000123977661},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4510999917984009},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.36890000104904175},{"id":"https://openalex.org/C168900304","wikidata":"https://www.wikidata.org/wiki/Q171407","display_name":"Valence (chemistry)","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C136643341","wikidata":"https://www.wikidata.org/wiki/Q1361526","display_name":"Reachability","level":2,"score":0.3165999948978424},{"id":"https://openalex.org/C206815938","wikidata":"https://www.wikidata.org/wiki/Q7077445","display_name":"Odd graph","level":5,"score":0.27239999175071716},{"id":"https://openalex.org/C6049932","wikidata":"https://www.wikidata.org/wiki/Q834981","display_name":"Graph automorphism","level":5,"score":0.2599000036716461}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/7588","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7588","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p6/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The Electronic Journal of Combinatorics","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1801.01106","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1801.01106","pdf_url":"https://arxiv.org/pdf/1801.01106","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"}],"best_oa_location":{"id":"doi:10.37236/7588","is_oa":true,"landing_page_url":"https://doi.org/10.37236/7588","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v26i2p6/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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","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/G2211149613","display_name":null,"funder_award_id":"J1-9108","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G4249711515","display_name":null,"funder_award_id":"J1-7051","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G6486294621","display_name":null,"funder_award_id":"J1-6720","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G6699426047","display_name":null,"funder_award_id":"N1-0038","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G8316966982","display_name":null,"funder_award_id":"N1-0032","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G8447924143","display_name":null,"funder_award_id":"P1-0285","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G8512759012","display_name":null,"funder_award_id":"11371307","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G8650182799","display_name":null,"funder_award_id":"N1-0062","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"},{"id":"https://openalex.org/G8982709776","display_name":null,"funder_award_id":"J1-9110","funder_id":"https://openalex.org/F4320322554","funder_display_name":"Javna Agencija za Raziskovalno Dejavnost RS"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"},{"id":"https://openalex.org/F4320322554","display_name":"Javna Agencija za Raziskovalno Dejavnost RS","ror":"https://ror.org/059bp8k51"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2782514139.pdf","grobid_xml":"https://content.openalex.org/works/W2782514139.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"A":[0],"graph":[1],"$\\Gamma$":[2],"of":[3,17,22,29,37,103,112,118,121,133,136,158,161,175,178],"even":[4],"order":[5],"is":[6,42,115,128,167,193],"a":[7,43,170],"bicirculant":[8],"if":[9],"it":[10],"admits":[11],"an":[12,172],"automorphism":[13,41],"with":[14,181],"two":[15,35],"orbits":[16,36],"equal":[18],"length.":[19],"Symmetry":[20],"properties":[21],"bicirculants,":[23],"for":[24,50,124],"which":[25,185],"at":[26,48],"least":[27,49],"one":[28],"the":[30,34,38,51,63,116,119,156,159],"induced":[31],"subgraphs":[32],"on":[33],"corresponding":[39,64],"semiregular":[40],"cycle,":[44],"have":[45,82],"been":[46,83],"studied,":[47],"few":[52],"smallest":[53],"possible":[54],"valences.":[55,126],"For":[56],"valences":[57],"$3$,":[58],"$4$":[59],"and":[60,74,94,140,164],"$5$,":[61],"where":[62],"bicirculants":[65,123],"are":[66,87,153],"called":[67],"generalized":[68,91],"Petersen":[69,92],"graphs,":[70,77,100],"Rose":[71,105],"window":[72,106],"graphs":[73,93,107,177],"Taba\u010d":[75,98],"jn":[76,99],"respectively,":[78],"all":[79],"edge-transitive":[80,90,97,104,134],"members":[81,152],"classified.":[84],"While":[85],"there":[86],"only":[88,95],"7":[89],"3":[96],"infinite":[101,131,173],"families":[102,132],"exist.":[108],"The":[109],"main":[110],"theme":[111],"this":[113],"paper":[114],"question":[117],"existence":[120],"such":[122],"higher":[125],"It":[127],"proved":[129],"that":[130],"examples":[135],"valence":[137,162,179],"$6$":[138,163,180],"exist":[139],"among":[141],"them":[142],"infinitely":[143,149],"many":[144,150],"arc-transitive":[145],"as":[146,148],"well":[147],"half-arc-transitive":[151,176],"identified.":[154],"Moreover,":[155],"classification":[157],"ones":[160],"girth":[165],"$3$":[166],"given.":[168],"As":[169],"corollary,":[171],"family":[174],"universal":[182],"reachability":[183],"relation,":[184],"were":[186],"thus":[187],"far":[188],"not":[189],"known":[190],"to":[191],"exist,":[192],"obtained.":[194]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2018-01-12T00:00:00"}
