{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T12:25:26Z","timestamp":1774355126337,"version":"3.50.1"},"reference-count":7,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2006,10,3]],"date-time":"2006-10-03T00:00:00Z","timestamp":1159833600000},"content-version":"vor","delay-in-days":8251,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1984,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Let <jats:italic>G<\/jats:italic> be a group acting symmetrically on a graph \u03a3, let <jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub> be a subgroup of <jats:italic>G<\/jats:italic> minimal among those that act symmetrically on \u03a3, and let <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub> be a subgroup of <jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub> maximal among those normal subgroups of <jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub> which contain no member except 1 which fixes a vertex of \u03a3. The most precise result of this paper is that if \u03a3 has prime valency <jats:italic>p<\/jats:italic>, then either \u03a3 is a bipartite graph or <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub> acts regularly on \u03a3 or <jats:italic>G<\/jats:italic><jats:sub>1<\/jats:sub> | <jats:italic>G<\/jats:italic><jats:sub>2<\/jats:sub> is a simple group which acts symmetrically on a graph of valency <jats:italic>p<\/jats:italic> which can be constructed from \u03a3 and does not have more vertices than \u03a3. The results on vertex\u2010transitive groups necessary to establish results like this are also included.<\/jats:p>","DOI":"10.1002\/jgt.3190080107","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T07:07:03Z","timestamp":1180422423000},"page":"55-68","source":"Crossref","is-referenced-by-count":128,"title":["Vertex\u2010transitive graphs: Symmetric graphs of prime valency"],"prefix":"10.1002","volume":"8","author":[{"given":"Peter","family":"Lorimer","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","volume-title":"Graph Theory with Applications","author":"Bondy J. A.","year":"1977"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511608704"},{"key":"e_1_2_1_4_2","volume-title":"The Fascination of Groups","author":"Budden F. J.","year":"1972"},{"key":"e_1_2_1_5_2","unstructured":"E. J.CockayneandS. T.Hedetnemi Graphes de groupes avec cliques maximales disjointes. In Probl\u00e8mes combinatoires et th\u00e9orie des graphes (Colloque International CNRS Universit\u00e9 Orsay Orsay 1976). CNRS Paris (1978)81 82."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-64981-3"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1007\/978-94-009-8489-9_11"},{"key":"e_1_2_1_8_2","volume-title":"Algebraic Theory of Graphs","author":"Teh H. H.","year":"1976"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190080107","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190080107","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,9,27]],"date-time":"2023-09-27T12:38:33Z","timestamp":1695818313000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190080107"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1984,3]]},"references-count":7,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1984,3]]}},"alternative-id":["10.1002\/jgt.3190080107"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190080107","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1984,3]]}}}