Contents Online
Mathematical Research Letters
Volume 17 (2010)
Number 2
Ricci curvature and eigenvalue estimate on locally finite graphs
Pages: 343 – 356
DOI: https://dx.doi.org/10.4310/MRL.2010.v17.n2.a13
Authors
Abstract
We give a generalizations of lower Ricci curvature bound in the framework of graphs. We prove that the Ricci curvature in the sense of Bakry and Emery is bounded below by $-1$ on locally finite graphs. The Ricci flat graph in the sense of Chung and Yau is proved to be a graph with Ricci curvature bounded below by zero. We also get an estimate for the eigenvalue of Laplace operator on finite graphs: $$\lambda\ge {1\over d D(\exp( d D+1)-1)},$$ where $d$ is the weighted degree of $G$, and $D$ is the diameter of $G$.
Published 1 January 2010