{"id":"https://openalex.org/W2063715612","doi":"https://doi.org/10.1002/jgt.3190080107","title":"Vertex\u2010transitive graphs: Symmetric graphs of prime valency","display_name":"Vertex\u2010transitive graphs: Symmetric graphs of prime valency","publication_year":1984,"publication_date":"1984-03-01","ids":{"openalex":"https://openalex.org/W2063715612","doi":"https://doi.org/10.1002/jgt.3190080107","mag":"2063715612"},"language":"en","primary_location":{"id":"doi:10.1002/jgt.3190080107","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190080107","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5110900671","display_name":"Peter Lorimer","orcid":null},"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":true,"raw_author_name":"Peter Lorimer","raw_affiliation_strings":["University of Auckland Auckland, New Zealand","UNIVERSITY OF AUCKLAND, Auckland, New Zealand"],"affiliations":[{"raw_affiliation_string":"University of Auckland Auckland, New Zealand","institution_ids":["https://openalex.org/I154130895"]},{"raw_affiliation_string":"UNIVERSITY OF AUCKLAND, Auckland, New Zealand","institution_ids":["https://openalex.org/I154130895"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110900671"],"corresponding_institution_ids":["https://openalex.org/I154130895"],"apc_list":{"value":3760,"currency":"USD","value_usd":3760},"apc_paid":null,"fwci":1.3624,"has_fulltext":false,"cited_by_count":183,"citation_normalized_percentile":{"value":0.77207977,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":96,"max":100},"biblio":{"volume":"8","issue":"1","first_page":"55","last_page":"68"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10849","display_name":"Finite Group Theory Research","score":0.9998999834060669,"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":0.9998999834060669,"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/T11130","display_name":"Coding theory and cryptography","score":0.9886999726295471,"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"}},{"id":"https://openalex.org/T11797","display_name":"graph theory and CDMA systems","score":0.9842000007629395,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/valency","display_name":"Valency","score":0.8957265019416809},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.8849139213562012},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8167644739151001},{"id":"https://openalex.org/keywords/vertex","display_name":"Vertex (graph theory)","score":0.6122766137123108},{"id":"https://openalex.org/keywords/bipartite-graph","display_name":"Bipartite graph","score":0.5393959879875183},{"id":"https://openalex.org/keywords/edge-transitive-graph","display_name":"Edge-transitive graph","score":0.4778535068035126},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4544258117675781},{"id":"https://openalex.org/keywords/transitive-relation","display_name":"Transitive relation","score":0.44669151306152344},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.44285815954208374},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.4327475428581238},{"id":"https://openalex.org/keywords/graph-power","display_name":"Graph power","score":0.19353383779525757},{"id":"https://openalex.org/keywords/line-graph","display_name":"Line graph","score":0.15580812096595764}],"concepts":[{"id":"https://openalex.org/C139007053","wikidata":"https://www.wikidata.org/wiki/Q1412952","display_name":"Valency","level":2,"score":0.8957265019416809},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.8849139213562012},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8167644739151001},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.6122766137123108},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.5393959879875183},{"id":"https://openalex.org/C200597783","wikidata":"https://www.wikidata.org/wiki/Q4391289","display_name":"Edge-transitive graph","level":5,"score":0.4778535068035126},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4544258117675781},{"id":"https://openalex.org/C191399111","wikidata":"https://www.wikidata.org/wiki/Q64861","display_name":"Transitive relation","level":2,"score":0.44669151306152344},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.44285815954208374},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.4327475428581238},{"id":"https://openalex.org/C149530733","wikidata":"https://www.wikidata.org/wiki/Q5597091","display_name":"Graph power","level":4,"score":0.19353383779525757},{"id":"https://openalex.org/C203776342","wikidata":"https://www.wikidata.org/wiki/Q1378376","display_name":"Line graph","level":3,"score":0.15580812096595764},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1002/jgt.3190080107","is_oa":false,"landing_page_url":"https://doi.org/10.1002/jgt.3190080107","pdf_url":null,"source":{"id":"https://openalex.org/S193368155","display_name":"Journal of Graph Theory","issn_l":"0364-9024","issn":["0364-9024","1097-0118"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320595","host_organization_name":"Wiley","host_organization_lineage":["https://openalex.org/P4310320595"],"host_organization_lineage_names":["Wiley"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Graph Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":6,"referenced_works":["https://openalex.org/W74866821","https://openalex.org/W1484040084","https://openalex.org/W1515707356","https://openalex.org/W2490728539","https://openalex.org/W3158061624","https://openalex.org/W4300303686"],"related_works":["https://openalex.org/W2237736622","https://openalex.org/W1988790461","https://openalex.org/W2107875203","https://openalex.org/W4232950734","https://openalex.org/W2352066879","https://openalex.org/W2103879540","https://openalex.org/W2384730381","https://openalex.org/W3143578817","https://openalex.org/W2969335708","https://openalex.org/W2038143369"],"abstract_inverted_index":{"Abstract":[0],"Let":[1],"G":[2,13,19,30,36,44,82,89,92],"be":[3,15,32,109],"a":[4,9,16,33,54,78,95,102],"group":[5,97],"acting":[6],"symmetrically":[7,25,100],"on":[8,26,86,101,123],"graph":[10,80,103],"\u03a3,":[11,27],"let":[12,29],"1":[14,37,45,51,90],"subgroup":[17,34],"of":[18,35,43,56,62,104],"minimal":[20],"among":[21,39],"those":[22,40],"that":[23,66],"act":[24],"and":[28,113],"2":[31,83,93],"maximal":[38],"normal":[41],"subgroups":[42],"which":[46,52,98,107],"contain":[47],"no":[48],"member":[49],"except":[50],"fixes":[53],"vertex":[55],"\u03a3.":[57,120],"The":[58,121],"most":[59],"precise":[60],"result":[61],"this":[63,131],"paper":[64],"is":[65,77,94],"if":[67],"\u03a3":[68,76,87,112],"has":[69],"prime":[70],"valency":[71,105],"p":[72,106],",":[73],"then":[74],"either":[75],"bipartite":[79],"or":[81,88],"acts":[84,99],"regularly":[85],"|":[91],"simple":[96],"can":[108],"constructed":[110],"from":[111],"does":[114],"not":[115],"have":[116],"more":[117],"vertices":[118],"than":[119],"results":[122,129],"vertex\u2010transitive":[124],"groups":[125],"necessary":[126],"to":[127],"establish":[128],"like":[130],"are":[132],"also":[133],"included.":[134]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":7},{"year":2020,"cited_by_count":5},{"year":2019,"cited_by_count":9},{"year":2018,"cited_by_count":8},{"year":2017,"cited_by_count":20},{"year":2016,"cited_by_count":15},{"year":2015,"cited_by_count":10},{"year":2014,"cited_by_count":8},{"year":2013,"cited_by_count":7},{"year":2012,"cited_by_count":7}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}
