{"title":"Ricci-flat graphs with maximum degree at most $4$","authors":"Shuliang Bai, Linyuan Lu, S. Yau","doi":"10.4310/ajm.2021.v25.n6.a1","DOIUrl":null,"url":null,"abstract":"A graph is called Ricci-flat if its Ricci curvatures vanish on all edges, here the definition of Ricci curvature on graphs was given by Lin-Lu-Yau [5]. The authors in [4] and [2] obtained a complete characterization for all Ricci-flat graphs with girth at least five. In this paper, we completely determined all Ricci-flat graphs with maximum degree at most 4. keywords: Ricci curvature, Ricci-flat graph, maximum degree","PeriodicalId":55452,"journal":{"name":"Asian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Asian Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4310/ajm.2021.v25.n6.a1","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 2
Abstract
A graph is called Ricci-flat if its Ricci curvatures vanish on all edges, here the definition of Ricci curvature on graphs was given by Lin-Lu-Yau [5]. The authors in [4] and [2] obtained a complete characterization for all Ricci-flat graphs with girth at least five. In this paper, we completely determined all Ricci-flat graphs with maximum degree at most 4. keywords: Ricci curvature, Ricci-flat graph, maximum degree
如果图的Ricci曲率在所有边上都消失，则称之为Ricci平坦图，这里图上Ricci曲率的定义是由Lin Lu Yau[5]给出的。作者在[4]和[2]中获得了所有周长至少为5的Ricci平面图的完整刻画。在本文中，我们完全确定了所有最大度为4的Ricci平面图。关键词：Ricci曲率，Ricci平面图，最大度
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
