TL;DR
This paper classifies all cubic graphs with non-negative Ollivier-Ricci or Bakry-Émery curvature, identifies prism graphs and Möbius ladders as the only such graphs, and introduces an online tool for curvature calculation.
Contribution
It provides a complete classification of non-negatively curved cubic graphs under two curvature notions and presents a new online tool for graph curvature computation.
Findings
Non-negatively curved cubic graphs are prism graphs and Möbius ladders.
Non-negatively curved cubic expanders do not exist.
An online tool for calculating graph curvature variants is introduced.
Abstract
We classify all cubic graphs with either non-negative Ollivier-Ricci curvature or non-negative Bakry-\'Emery curvature everywhere. We show in both curvature notions that the non-negatively curved graphs are the prism graphs and the M\"obius ladders. We also highlight an online tool for calculating the curvature of graphs under several variants of these curvature notions that we use in the classification. As a consequence of the classification result we show, that non-negatively curved cubic expanders do not exist.
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