22 papers · 1 filter
An extremal theorem for positive curvature of graphs
Kaizhe Chen, Shiping Liu, Zhe You
We prove an extremal theorem for positive Ollivier/Lin--Lu--Yau curvature: every graph of order \(n\geq 8\) with more than \[ T(n)=\frac{n^2-3n}{2}-\left\lceil\frac{n}{2}\right\rce…
New bounds for equiangular lines and Balla's conjecture
Chuanyuan Ge, Shiping Liu
Let denote the maximum number of equiangular lines in with common angle . Balla conjectured that, if the spectral radius order $κ_{\frac{1-α…
On Lichnerowicz sharp distance-regular graphs
Kaizhe Chen, Shiping Liu, Heng Zhang
The first non-zero Laplacian eigenvalue of a finite graph is bounded below by its minimum Lin--Lu--Yau curvature . This is a discrete analogue of the classical Lichnerow…
Criteria on forbidden subgraphs in the complements for positive Lin--Lu--Yau curvature
Kaizhe Chen, Shiping Liu, Zhe You
We investigate forbidden subgraph conditions in the complement of a graph that guarantee positive Lin--Lu--Yau curvature. In particular, we prove that every graph whose complement…
Edge-connectivity and non-negative Lin-Lu-Yau curvature
Shiping Liu, Qing Xia
By definition, the edge-connectivity of a connected graph is no larger than its minimum degree. In this paper, we prove that the edge connectivity of a finite connected graph with…
Discrete Bakry-Ãmery curvature tensors and matrices of connection graphs
Chunyang Hu, Shiping Liu
Liu, Münch, and Peyerimhoff introduced the notion of Bakry-Ãmery curvature for connection graphs as a means to derive Buser-type bounds on the eigenvalues of connection Laplacian…