{"title":"On neighborhoods in the enhanced power graph associated with a finite group","authors":"Mark L. Lewis, Carmine Monetta","doi":"arxiv-2408.16545","DOIUrl":null,"url":null,"abstract":"This article investigates neighborhoods' sizes in the enhanced power graph\n(as known as the cyclic graph) associated with a finite group. In particular,\nwe characterize finite $p$-groups with the smallest maximum size for\nneighborhoods of nontrivial element in its enhanced power graph.","PeriodicalId":501037,"journal":{"name":"arXiv - MATH - Group Theory","volume":"9 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Group Theory","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.16545","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
This article investigates neighborhoods' sizes in the enhanced power graph
(as known as the cyclic graph) associated with a finite group. In particular,
we characterize finite $p$-groups with the smallest maximum size for
neighborhoods of nontrivial element in its enhanced power graph.
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