Graphs with Positive Ricci Curvature

In this paper, we study the Ricci curvature defined by Yong Lin, Linyuan Lu and Shing-Tung Yau, and characterize several graphs with constant positive Ricci curvature. We find the necessary and sufficient condition when every edge of the graph has Ricci curvature no less than one and characterize the graphs in which the Ricci curvature of every edge is equal to one. Moreover, we study the graphs with constant Ricci curvature \(\frac{n-4}{n-3}\) $\frac{n-4}{n-3}$ , where n is the number of vertices.