English

Ricci-flat graphs with girth four

Combinatorics 2018-07-20 v1 Differential Geometry

Abstract

Lin-Lu-Yau introduced an interesting notion of Ricci curvature for graphs and obtained a complete characterization for all Ricci-flat graphs with girth at least five [1]. In this paper, we propose a concrete approach to construct an infinite family of distinct Ricci-flat graphs of girth four with edge-disjoint 4-cycles and completely characterize all Ricci-flat graphs of girth four with vertex-disjoint 4-cycles.

Keywords

Cite

@article{arxiv.1807.07253,
  title  = {Ricci-flat graphs with girth four},
  author = {Weihua He and Jun Luo and Chao Yang and Wei Yuan},
  journal= {arXiv preprint arXiv:1807.07253},
  year   = {2018}
}
R2 v1 2026-06-23T03:06:54.099Z