We give a classification of all connected quartic graphs which are (infinity) curvature sharp in all vertices with respect to Bakry-\'Emery curvature. The result is based on a computer classification by F. Gurr and L. Watson May and a combinatorial case by case investigation.
@article{arxiv.1902.10665,
title = {Quartic graphs which are Bakry-\'Emery curvature sharp},
author = {David Cushing and Supanat Kamtue and Norbert Peyerimhoff and Leyna Watson May},
journal= {arXiv preprint arXiv:1902.10665},
year = {2019}
}