Asian Journal of Mathematics
Volume 25 (2021)
Ricci-flat graphs with maximum degree at most $4$
Pages: 757 – 814
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  and  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 $4$.
Ricci curvature, Ricci-flat graph, graph construction
2010 Mathematics Subject Classification
The second-named author was supported in part by NSF grant DMS 1600811 and ONR grant N00014-17-1-2842.
The third-named author was supported by NSF grant DMS-1607871: Analysis, Geometry and Mathematical Physics; and by NSF grant DMS-1418252, Collaborative Research: Geometric Analysis for Computer and Social Networks.
Received 28 November 2018
Accepted 25 June 2021
Published 24 October 2022