{"id":"https://openalex.org/W1606003972","doi":"https://doi.org/10.37236/4013","title":"On Embeddings of Circulant Graphs","display_name":"On Embeddings of Circulant Graphs","publication_year":2015,"publication_date":"2015-05-22","ids":{"openalex":"https://openalex.org/W1606003972","doi":"https://doi.org/10.37236/4013","mag":"1606003972"},"language":"en","primary_location":{"id":"doi:10.37236/4013","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4013","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p28/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":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p28/pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5061875089","display_name":"Marston Conder","orcid":"https://orcid.org/0000-0002-0256-6978"},"institutions":[{"id":"https://openalex.org/I154130895","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07","country_code":"NZ","type":"education","lineage":["https://openalex.org/I154130895"]}],"countries":["NZ"],"is_corresponding":false,"raw_author_name":"Marston Conder","raw_affiliation_strings":["University of Auckland","University of AUCKLAND"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Auckland","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"University of AUCKLAND","institution_ids":["https://openalex.org/I154130895"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5009530856","display_name":"Ricardo Grande","orcid":"https://orcid.org/0000-0002-1521-6790"},"institutions":[{"id":"https://openalex.org/I169108374","display_name":"University of the Basque Country","ror":"https://ror.org/000xsnr85","country_code":"ES","type":"education","lineage":["https://openalex.org/I169108374"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Ricardo Grande","raw_affiliation_strings":["University of the Basque Country","University of The Basque Country"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of the Basque Country","institution_ids":["https://openalex.org/I169108374"]},{"raw_affiliation_string":"University of The Basque Country","institution_ids":["https://openalex.org/I169108374"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.6325,"has_fulltext":true,"cited_by_count":13,"citation_normalized_percentile":{"value":0.86393145,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"22","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":0.9987000226974487,"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":0.9987000226974487,"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":0.9983000159263611,"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/T10829","display_name":"Interconnection Networks and Systems","score":0.9962999820709229,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8402627110481262},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7792782187461853},{"id":"https://openalex.org/keywords/circulant-matrix","display_name":"Circulant matrix","score":0.6675448417663574},{"id":"https://openalex.org/keywords/cayley-graph","display_name":"Cayley graph","score":0.6604365110397339},{"id":"https://openalex.org/keywords/genus","display_name":"Genus","score":0.5635372400283813},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.5237643122673035},{"id":"https://openalex.org/keywords/planar-graph","display_name":"Planar graph","score":0.42258816957473755},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.4195522665977478},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.416415810585022},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3834584355354309},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.09909436106681824}],"concepts":[{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8402627110481262},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7792782187461853},{"id":"https://openalex.org/C115973184","wikidata":"https://www.wikidata.org/wiki/Q245457","display_name":"Circulant matrix","level":2,"score":0.6675448417663574},{"id":"https://openalex.org/C120204988","wikidata":"https://www.wikidata.org/wiki/Q859174","display_name":"Cayley graph","level":3,"score":0.6604365110397339},{"id":"https://openalex.org/C157369684","wikidata":"https://www.wikidata.org/wiki/Q34740","display_name":"Genus","level":2,"score":0.5635372400283813},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.5237643122673035},{"id":"https://openalex.org/C101837359","wikidata":"https://www.wikidata.org/wiki/Q547823","display_name":"Planar graph","level":3,"score":0.42258816957473755},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.4195522665977478},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.416415810585022},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3834584355354309},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.09909436106681824},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C59822182","wikidata":"https://www.wikidata.org/wiki/Q441","display_name":"Botany","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.37236/4013","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4013","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p28/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:HAL:hal-03468472v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03468472","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The Electronic Journal of Combinatorics, 2015, 22 (2), &#x27E8;10.37236/4013&#x27E9;","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.37236/4013","is_oa":true,"landing_page_url":"https://doi.org/10.37236/4013","pdf_url":"https://www.combinatorics.org/ojs/index.php/eljc/article/download/v22i2p28/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/G6750727205","display_name":null,"funder_award_id":"UOA 1015","funder_id":"https://openalex.org/F4320335369","funder_display_name":"Marsden Fund"}],"funders":[{"id":"https://openalex.org/F4320320801","display_name":"University of Auckland","ror":"https://ror.org/03b94tp07"},{"id":"https://openalex.org/F4320321919","display_name":"Euskal Herriko Unibertsitatea","ror":"https://ror.org/000xsnr85"},{"id":"https://openalex.org/F4320335369","display_name":"Marsden Fund","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1606003972.pdf","grobid_xml":"https://content.openalex.org/works/W1606003972.grobid-xml"},"referenced_works_count":17,"referenced_works":["https://openalex.org/W1529310515","https://openalex.org/W1534001760","https://openalex.org/W1558273801","https://openalex.org/W1573025956","https://openalex.org/W1605696684","https://openalex.org/W1969308201","https://openalex.org/W1976677460","https://openalex.org/W1995632106","https://openalex.org/W1998391578","https://openalex.org/W2018280788","https://openalex.org/W2020422308","https://openalex.org/W2058555041","https://openalex.org/W2059799590","https://openalex.org/W2088455492","https://openalex.org/W2578484701","https://openalex.org/W4234586542","https://openalex.org/W6813186015"],"related_works":["https://openalex.org/W2117159910","https://openalex.org/W2335757200","https://openalex.org/W2049656902","https://openalex.org/W2044900700","https://openalex.org/W2549019542","https://openalex.org/W2139378013","https://openalex.org/W2099807911","https://openalex.org/W2069171014","https://openalex.org/W4312183368","https://openalex.org/W2244024694"],"abstract_inverted_index":{"A":[0],"circulant":[1],"of":[2,21,31,54,95],"order":[3],"$n$":[4],"is":[5],"a":[6,18,52],"Cayley":[7],"graph":[8],"for":[9,68],"the":[10,40],"cyclic":[11],"group":[12],"$\\mathbb{Z}_n$,":[13],"and":[14,50,90,103],"as":[15],"such,":[16],"admits":[17],"transitive":[19],"action":[20],"$\\mathbb{Z}_n$":[22],"on":[23,34,39],"its":[24],"vertices.":[25],"This":[26],"paper":[27],"concerns":[28],"2-cell":[29],"embeddings":[30],"connected":[32,80],"circulants":[33,81,98],"closed":[35],"orientable":[36],"surfaces.":[37],"Embeddings":[38],"sphere":[41],"(the":[42],"planar":[43],"case)":[44],"were":[45],"classified":[46],"by":[47,51,99],"Heuberger":[48],"(2003),":[49],"theorem":[53],"Thomassen":[55],"(1991),":[56],"there":[57],"are":[58],"only":[59],"finitely":[60],"many":[61],"vertex-transitive":[62],"graphs":[63],"with":[64,82],"minimum":[65,83],"genus":[66,84],"$g$,":[67],"any":[69],"given":[70],"integer":[71],"$g":[72],"\\ge":[73],"3$.":[74],"Here":[75],"we":[76],"completely":[77],"determine":[78],"all":[79,96],"1":[85],"or":[86],"2;":[87],"this":[88],"corrects":[89],"extends":[91],"an":[92],"attempted":[93],"classification":[94],"toroidal":[97],"Costa,":[100],"Strapasson,":[101],"Alves":[102],"Carlos":[104],"(2010).":[105]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":2},{"year":2016,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
