{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,11,13]],"date-time":"2023-11-13T00:32:05Z","timestamp":1699835525661},"reference-count":9,"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":8982,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Journal of Graph Theory"],"published-print":{"date-parts":[[1982,3]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>If <jats:italic>n<\/jats:italic> is divisible by at least three distinct primes, the dihedral group <jats:italic>D<jats:sub>n<\/jats:sub><\/jats:italic> can be generated by three nonredundant, involuntary elements. We study the Cayley graphs resulting from such a presentation of <jats:italic>D<jats:sub>n<\/jats:sub><\/jats:italic> for several families of <jats:italic>n<\/jats:italic> and for all admissible <jats:italic>n<\/jats:italic> &lt; 120. All these graphs are trivalent, bipartite, Hamiltonian, of girth 6, and are regular representations of their groups. For each <jats:italic>n<\/jats:italic>, the isomorphism classes are determined and the graphs are described by a simple code.<\/jats:p>","DOI":"10.1002\/jgt.3190060106","type":"journal-article","created":{"date-parts":[[2007,5,29]],"date-time":"2007-05-29T06:33:48Z","timestamp":1180420428000},"page":"43-55","source":"Crossref","is-referenced-by-count":3,"title":["Exceptional trivalent cayley graphs for dihedral groups"],"prefix":"10.1002","volume":"6","author":[{"given":"David L.","family":"Powers","sequence":"first","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2006,10,3]]},"reference":[{"key":"e_1_2_1_2_2","unstructured":"B.AlspachandT. D.Parsons A construction for vertex\u2010transitive graphs. Preprint."},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1979.tb32769.x"},{"key":"e_1_2_1_4_2","unstructured":"T. G.Boreham Some Uses of the Paths of Graphs in Determining Their Groups. Ph.D. Thesis University of New Brunswick 1974."},{"key":"e_1_2_1_5_2","first-page":"213","volume-title":"Graphs and Combinatorics, Lecture Notes in Mathematics No. 406","author":"Boreham T. G.","year":"1974"},{"key":"e_1_2_1_6_2","unstructured":"H. S. M.Coxeter Twisted Honeycombs C.B.M.S. Regional Conference Series in Math. No. 4 1970."},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1111\/j.1749-6632.1970.tb56466.x"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1002\/jgt.3190010111"},{"key":"e_1_2_1_9_2","doi-asserted-by":"publisher","DOI":"10.1016\/0095-8956(71)90019-0"},{"key":"e_1_2_1_10_2","volume-title":"Graphs, Groups and Surfaces","author":"White A. T.","year":"1973"}],"container-title":["Journal of Graph Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Fjgt.3190060106","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/jgt.3190060106","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,11,12]],"date-time":"2023-11-12T05:15:01Z","timestamp":1699766101000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/jgt.3190060106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,3]]},"references-count":9,"journal-issue":{"issue":"1","published-print":{"date-parts":[[1982,3]]}},"alternative-id":["10.1002\/jgt.3190060106"],"URL":"https:\/\/doi.org\/10.1002\/jgt.3190060106","archive":["Portico"],"relation":{},"ISSN":["0364-9024","1097-0118"],"issn-type":[{"value":"0364-9024","type":"print"},{"value":"1097-0118","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,3]]}}}