121 citations · 538 across the 72 of their papers we have counts for
13 papers · 1 filter
Auslander-Reiten theory via Nakayama duality in abelian categories
Zetao Lin, Shiping Liu
Using the Nakayama duality induced by a Nakayama functor, we provide a novel and concise account of the existence of Auslander-Reiten dualities and almost split sequences in abelia…
A new proof of the Lemmens-Seidel conjecture
Chuanyuan Ge, Shiping Liu
In this paper, we give a new proof of the Lemmens-Seidel conjecture on the maximum number of equiangular lines with a common angle . This conjecture was previously re…
A generalized Cheeger inequality and the Steklov Problem on finite graphs
Bobo Hua, Supanat Kamtue, Shiping Liu +2
We prove generalized Cheeger inequalities for eigenvalues of Laplacians for reversible Markov chains. Then we apply Hassannezhad and Miclo's convergence result to obtain Jammes Che…
Quantitative Obata's theorem in discrete setting
Shiping Liu, Chiyu Zhou
Under mild assumptions, we show that a connected weighted graph with lower Ricci curvature bound in the sense of Bakry-Émery and the -th non-zero Laplacian eigenvalue…
On finiteness of spectral radius order
Yanlong Ding, Chuanyuan Ge, Shiping Liu
The concept of spectral radius order plays an crucial role in the breakthrough work on equiangular lines due to Jiang, Tidor, Yao, Zhang, and Zhao [Ann. of Math. (2) 194 (2021), no…
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…
Edge-connectivity of graphs with non-negative Bakry-Émery curvature and amply regular graphs
Kaizhe Chen, Jack H. Koolen, Shiping Liu
We establish a sharp edge-connectivity estimate for graphs with non-negative Bakry-Émery curvature. This leads to a geometric criterion for the existence of a perfect matching. Pre…
Equiangular lines via nodal domains
Chuanyuan Ge, Shiping Liu
For given and , we show that the maximum multiplicity that can appear as the second largest eigenvalue of a connected graph with maximum degree at most $Δ…
On a magneto-spectral invariant on finite graphs
Chunyang Hu, Bobo Hua, Supanat Kamtue +3
In this paper, we introduce a magneto-spectral invariant for finite graphs. This invariant vanishes on trees and is maximized by complete graphs. We compute this invariant for cycl…
Representation theory of hereditary artin algebras of finite representation type
Shiping Liu, Gordana Todorov
Let be a hereditary artin algebra of finite representation type. We first determine all hammocks in the Auslander-Reiten quiver $\GaH$ of $\mmod H$, the category of finitely ge…
Halin graphs with positive Lin-Lu-Yau curvature
Kaizhe Chen, Huiqiu Lin, Shiping Liu +1
Halin graphs constitute an interesting class of planar and polyhedral graphs. A generalized Halin graph is obtained by connecting all leaves of a planar embedding of a tree via a c…
Monotonic normalized heat diffusion for distance-regular graphs with classical parameters of diameter
Shiping Liu, Heng Zhang
We prove the monotonic normalized heat diffusion property on distance-regular graphs with classical parameters of diameter . Regev and Shinkar found a Cayley graph for which thi…
Connectivity versus Lin-Lu-Yau curvature
Kaizhe Chen, Shiping Liu, Zhe You
We explore the interaction between connectivity and Lin-Lu-Yau curvature of graphs systematically. The intuition is that connected graphs with large Lin-Lu-Yau curvature also have…