Ricci-flat graphs with girth at least five

被引：22

作者：

Lin, Yong ^{[1
]}

Lu, Linyuan ^{[2
]}

Yau, S. -T. ^{[3
]}

机构：

[1] Renmin Univ China, Beijing 100872, Peoples R China

[2] Univ S Carolina, Columbia, SC 29208 USA

[3] Harvard Univ, Cambridge, MA 02138 USA

来源：

COMMUNICATIONS IN ANALYSIS AND GEOMETRY | 2014年 / 22卷 / 04期

基金：

美国国家科学基金会; 中国国家自然科学基金;

关键词：

METRIC-MEASURE-SPACES; CURVATURE; DISCRETE;

D O I：

10.4310/CAG.2014.v22.n4.a3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A graph is called Ricci-flat if its Ricci curvatures vanish on all edges. Here we use the definition of Ricci curvature on graphs given in Lin-Lu-Yau, Tohoku Math., 2011, which is a variation of Ollivier, J. Funct. Math., 2009. In this paper, we classified all Ricci-fiat connected graphs with girth at least five: they are the infinite path, cycle C-n (n >= 6), the dodecahedral graph, the Petersen graph and the half-dodecahedral graph. We also construct many Ricci-flat graphs with girth 3 or 4 by using the root systems of simple Lie algebras.

引用

页码：671 / 687

页数：17

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