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}
}