围长至少为5的Ricci平坦图
Ricci-flat graphs with girth at least five
摘要：
如果一个图的所有边的Ricci曲率为零，则称该图为Ricci平坦图。在这里，我们使用[Lin-Lu-Yau，Tohoku Math.，2011]，其是[Ollivier，J. Funct.数学，2009年]。本文将围长至少为5的Ricci-平坦连通图分类为：无限路、圈$C_n$（$n\geq 6$）、十二面体图、Petersen图和半十二面体图。我们还利用简单李代数的根系构造了许多围长为3或4的Ricci平坦图。
英文摘要：
A graph is called Ricci-flat if its Ricci-curvatures vanish on all edges. Here we use the definition of Ricci-cruvature 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-flat connected graphs with girth at least five: they are the infinite path, cycle $C_n$ ($n\geq 6$), 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.
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