From the 1 of 7 linked papers with an AI index.
7 papers
Discrete Einstein metrics on unicyclic graphs
Shuliang Bai
The paper extends the study of discrete Einstein metrics defined via Lin‑Lu‑Yau curvature from trees to unicyclic graphs, identifying when the tree‑based solution persists, providi…
Discrete Einstein metrics on trees
Shuliang Bai, Haoxuan Cheng, Bobo Hua
We establish the existence and uniqueness of discrete Einstein metrics on trees under Lin-Lu-Yau Ricci curvature using Perron-Frobenius theory. We establish a sharp upper bound for…
Edge Subdivision and the Perron Eigenvalue of Tree Ricci Matrices
Shuliang Bai, Haoxuan Cheng, Bobo Hua
The Ricci matrix of a finite tree encodes its discrete Einstein metrics via the Perron eigenvector, with Lin-Lu-Yau's Ollivier Ricci curvature: . We show…
Spectral Monotonicity under Leaf Attachment and Limiting Behavior in Discrete Einstein Trees
Shuliang Bai, Haoxuan Cheng, Bobo Hua
Let be the Ricci matrix of a finite tree introduced in \cite{BaiChengHua2026}, the largest eigenvalue determines the sign of a discrete Einstein metric c…
On the Ricci flow on Trees
Shuliang Bai, Bobo Hua, Yong Lin +1
In this paper, we study the evolution of metrics on finite trees under continuous-time Ricci flows based on the Lin-Lu-Yau version of Ollivier Ricci curvature. We analyze long-time…
The weighted Forman and Lin-Lu-Yau Ricci flow on graphs
Shuliang Bai, Shuang Liu, Xin Lai
In this paper, we propose a type of Ricci flow on graphs where the probability distribution for the Lin-Lu-Yau curvature remains constant over time, and also study the related Form…