The Graph Curvature Calculator and the curvatures of cubic graphs
Combinatorics
2023-10-26 v2
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.
Keywords
Cite
@article{arxiv.1712.03033,
title = {The Graph Curvature Calculator and the curvatures of cubic graphs},
author = {David Cushing and Riikka Kangaslampi and Valtteri Lipiäinen and Shiping Liu and George William Stagg},
journal= {arXiv preprint arXiv:1712.03033},
year = {2023}
}