121 citations · 538 across the 72 of their papers we have counts for
11 papers · 1 filter
Diameter bounds for distance-regular graphs via long-scale Ollivier Ricci curvature
Kaizhe Chen, Shiping Liu
In this paper, we derive new sharp diameter bounds for distance regular graphs, which better answer a problem raised by Neumaier and Penji\' c in many cases. Our proof is built upo…
A Representation theoretic perspective of Koszul theory
Ales Bouhada, Min Huang, Zetao Lin +1
We discover a new connection between Koszul theory and representation theory. Let $\La$ be a quadratic algebra defined by a locally finite quiver with relations. Firstly, we give a…
Polyhedral volume ratios, Izmestiev's Colin de Verdiere matrices and Spectral Gaps
Ioannis Ivrissimtzis, Carsten Lange, Shiping Liu +1
We present a relation between volumes of certain lower dimensional simplices associated to a full-dimensional primal and polar dual polytope in R^k. We then discuss an application…
Ricci curvature, diameter and eigenvalues of amply regular graphs
Kaizhe Chen, Chunyang Hu, Shiping Liu +1
Amply regular graphs are graphs with local distance-regularity constraints. In this paper, we prove a weaker version of a conjecture proposed by Qiao, Park, and Koolen on diameter…
Representation theory of graded algebras given by locally finite quivers
Zetao Lin, Shiping Liu
This paper aims to study graded modules over a graded algebra $\La$ given by a locally finite quiver with homogeneous relations. By constructing a graded Nakayama functor, we disco…
Curvature and local matchings of conference graphs and extensions
Kaizhe Chen, Shiping Liu, Heng Zhang
We prove a conjecture of Bonini et al. on the precise values of the Lin--Lu--Yau curvature of conference graphs, i.e., strongly regular graphs with parameters . Ou…
Discrete trace formulas and holomorphic functional calculus for the adjacency matrix of regular graphs
Yulin Gong, Wenbo Li, Shiping Liu
We provide a unified method to study the adjacency matrices of regular graphs (including infinite ones) using holomorphic functional calculus. By applying this calculus on a specif…
Spectral convergence of random regular graphs: Chebyshev polynomials, non-backtracking walks, and unitary-color extensions
Yulin Gong, Wenbo Li, Shiping Liu
In this paper, we give a short proof of the weak convergence to the Kesten-McKay distribution for the normalized spectral measures of random -lifts. This result is derived by ge…
A note on Steinerberger's curvature for graphs
David Cushing, Supanat Kamtue, Erin Law +3
In this note, we provide Steinerberger curvature formulas for block graphs, discuss curvature relations between two graphs and the graph obtained by connecting them via a bridge, a…
Curvature, diameter and signs of graphs
Wei Chen, Shiping Liu
We prove a Li-Yau type eigenvalue-diameter estimate for signed graphs. That is, the nonzero eigenvalues of the Laplacian of a non-negatively curved signed graph are lower bounded b…
Entropic curvature not comparable to other curvatures -- or is it?
Supanat Kamtue, Shiping Liu, Florentin Münch +1
In this paper we consider global -curvatures of finite Markov chains with associated means in the spirit of the entropic curvature (based on the logarithmic mean) by Erbar-M…