Zobrazeno 1 - 10
of 884
pro vyhledávání: '"Liu, Shiping"'
We prove a weaker version of a conjecture proposed by Qiao, Park and Koolen on diameter bounds of amply regular graphs and make new progress on Terwilliger's conjecture on finiteness of amply regular graphs. We achieve these results by a significantl
Externí odkaz:
http://arxiv.org/abs/2410.21055
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 of this relation to a geometric construction of a Colin de Verdiere ma
Externí odkaz:
http://arxiv.org/abs/2410.02494
Autor:
Lin, Zetao, Liu, Shiping
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 discover a novel approach to establish Auslander-Reiten formulas, from whic
Externí odkaz:
http://arxiv.org/abs/2409.20392
We confirm a conjecture of Bonini et. al. on the precise Lin-Lu-Yau curvature values of conference graphs, i.e., strongly regular graphs with parameters $(4\gamma+1,2\gamma,\gamma-1,\gamma)$, with $\gamma\geq 2$. Our method only depends on the parame
Externí odkaz:
http://arxiv.org/abs/2409.06418
We study the holomorphic functional calculus for the adjacency matrices on possibly infinite regular graphs. More precisely, we show an expansion of $h(A)$ in terms of non-backtracking matrices, where $A$ is the adjacency matrix and $h$ is a holomorp
Externí odkaz:
http://arxiv.org/abs/2406.17505
In this paper, we give a short proof of the weak convergence to the Kesten-McKay distribution for the normalized spectral measures of random $N$-lifts. This result is derived by generalizing a formula of Friedman involving Chebyshev polynomials and n
Externí odkaz:
http://arxiv.org/abs/2406.05759
Autor:
Cushing, David, Kamtue, Supanat, Law, Erin, Liu, Shiping, Münch, Florentin, Peyerimhoff, Norbert
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, and show that self-centered Bonnet-Myers sharp graphs are precisely tho
Externí odkaz:
http://arxiv.org/abs/2404.17860
Autor:
Chen, Wei, Liu, Shiping
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 by $1/D^2$ up to a constant, where $D$ stands for the diameter. This le
Externí odkaz:
http://arxiv.org/abs/2404.15594
In this paper we consider global $\theta$-curvatures of finite Markov chains with associated means $\theta$ in the spirit of the entropic curvature (based on the logarithmic mean) by Erbar-Maas and Mielke. As in the case of Bakry-\'Emery curvature, w
Externí odkaz:
http://arxiv.org/abs/2404.04581
In this paper, we propose a generalization of Bakry-\'Emery's calculus which allows us to formulate both Bakry-\'Emery and entropic curvature simultaneously. This formulation represents both curvatures as an integral of the Bochner formula against so
Externí odkaz:
http://arxiv.org/abs/2312.09686