We classify all cubic graphs with either non-negative Ollivier-Riccicurvature or non-negative Bakry-'Emery curvature everywhere. We show in bothcurvature notions that the non-negatively curved graphs are the prism graphsand the M"obius ladders. We also highlight an online tool for calculating thecurvature of graphs under several variants of these curvature notions that weuse in the classification. As a consequence of the classification result weshow, that non-negatively curved cubic expanders do not exist.
展开▼
