2024/09/24 by Li, Yupei, Lu, Linyuan
#05C10 #53A70 #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2409.15667
In this paper, we establish a simple formula for computing the Lin-Lu-Yau Ricci curvature on graphs. For any edge xy in a simple locally finite graph G, the curvature κ(x,y) can be expressed as a cost function of an optimal bijection between two blow-up sets of the neighbors of x and y. Utilizing this approach, we derive several results including a structural theorem for the Bonnet-Myers sharp irregular graphs of diameter 3 and a theorem on C3-free Bonnet-Myers sharp graphs.