2018/07/19 by Weihua He, Jun Luo, He, Weihua +5
Mathematics · #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #math.CO #math.DG
paper · pdf · doi:10.48550/arxiv.1807.07253
arxiv created 2018/07/19 · arxiv updated 2018/07/20
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.