Ricci-flat graphs with maximum degree at most 4

Abstract

A graph is called Ricci-flat if its Ricci curvatures vanish on all edges, here the definition of Ricci curvature on graphs was given by Lin-Lu-Yau. The authors in arXiv:1301.0102 and arXiv:1802.02982 obtained a complete characterization for all Ricci-flat graphs with girth at least five. In this paper, we completely determined all Ricci-flat graphs with maximum degree at most 4.

Notes of Ricci flat graphs with maximum degree at most 4.Proofs are in separated notes

References in corpus (2)

• Ricci-flat cubic graphs with girth five
• Ricci-flat graphs with girth four

Cited by in corpus (2)

• Graph Laplacians, Riemannian Manifolds and their Machine-Learning
• Graphs with nonnegative Ricci curvature and maximum degree at most 3