最大度不超过$4的里奇平坦图

IF 0.5 4区数学 Q3 MATHEMATICS Asian Journal of Mathematics Pub Date : 2021-03-01 DOI:10.4310/ajm.2021.v25.n6.a1

Shuliang Bai, Linyuan Lu, S. Yau

{"title":"最大度不超过$4的里奇平坦图","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":" ","pages":""},"PeriodicalIF":0.5000,"publicationDate":"2021-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"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\":\" \",\"pages\":\"\"},\"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}","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

摘要

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

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Ricci-flat graphs with maximum degree at most $4$

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

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊