{"title":"Petersen图的自同构群与$S_5$同构。","authors":"J. Wood","doi":"10.4169/math.mag.89.4.267","DOIUrl":null,"url":null,"abstract":"The automorphism group of the Petersen Graph is shown to be isomorphic to the symmetric group on 5 elements. The image represents the Petersen Graph with the ten 3-element subsets of $\\{1, 2, 3, 4, 5\\}$ as vertices. Two vertices are adjacent when they have precisely one element in common.","PeriodicalId":429168,"journal":{"name":"arXiv: History and Overview","volume":"9 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"The Automorphism Group of the Petersen Graph is Isomorphic to $S_5$.\",\"authors\":\"J. Wood\",\"doi\":\"10.4169/math.mag.89.4.267\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The automorphism group of the Petersen Graph is shown to be isomorphic to the symmetric group on 5 elements. The image represents the Petersen Graph with the ten 3-element subsets of $\\\\{1, 2, 3, 4, 5\\\\}$ as vertices. Two vertices are adjacent when they have precisely one element in common.\",\"PeriodicalId\":429168,\"journal\":{\"name\":\"arXiv: History and Overview\",\"volume\":\"9 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-12-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv: History and Overview\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4169/math.mag.89.4.267\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: History and Overview","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4169/math.mag.89.4.267","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
The Automorphism Group of the Petersen Graph is Isomorphic to $S_5$.
The automorphism group of the Petersen Graph is shown to be isomorphic to the symmetric group on 5 elements. The image represents the Petersen Graph with the ten 3-element subsets of $\{1, 2, 3, 4, 5\}$ as vertices. Two vertices are adjacent when they have precisely one element in common.
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