{"title":"The diameter of a random Cayley graph of ℤ q","authors":"Gideon Amir, O. Gurel-Gurevich","doi":"10.1515/gcc.2010.004","DOIUrl":null,"url":null,"abstract":"Abstract Consider the Cayley graph of the cyclic group of prime order q with k uniformly chosen generators. For fixed k, we prove that the diameter of said graph is asymptotically (in q) of order . This answers a question of Benjamini. The same also holds when the generating set is taken to be a symmetric set of size 2k.","PeriodicalId":119576,"journal":{"name":"Groups Complex. Cryptol.","volume":"14 1-2","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2010-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"12","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Groups Complex. Cryptol.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/gcc.2010.004","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 12
Abstract
Abstract Consider the Cayley graph of the cyclic group of prime order q with k uniformly chosen generators. For fixed k, we prove that the diameter of said graph is asymptotically (in q) of order . This answers a question of Benjamini. The same also holds when the generating set is taken to be a symmetric set of size 2k.
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