# Quartic graphs which are Bakry-\'Emery curvature sharp

## TL;DR

This paper classifies all connected quartic graphs that are curvature sharp in the Bakry-Émery sense at every vertex, combining computational and combinatorial methods.

## Contribution

It provides a complete classification of quartic graphs with uniform Bakry-Émery curvature sharpness, extending understanding of curvature properties in graph theory.

## Key findings

- Identified all connected quartic curvature sharp graphs
- Combined computational classification with combinatorial analysis
- Established criteria for curvature sharpness in quartic graphs

## Abstract

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.