121 citations · 538 across the 72 of their papers we have counts for
11 papers · 1 filter
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…
New graph invariants based on -Laplacian eigenvalues
Chuanyuan Ge, Shiping Liu, Dong Zhang
We present monotonicity inequalities for certain functions involving eigenvalues of -Laplacians on signed graphs with respect to . Inspired by such monotonicity, we propose n…
Nodal domain theorems for -Laplacians on signed graphs
Chuanyuan Ge, Shiping Liu, Dong Zhang
We establish various nodal domain theorems for -Laplacians on signed graphs, which unify most of the existing results on nodal domains of graph -Laplacians and arbitrary symm…
Symmetric Matrices, Signed Graphs, and Nodal Domain Theorems
Chuanyuan Ge, Shiping Liu
In 2001, Davies, Gladwell, Leydold, and Stadler proved discrete nodal domain theorems for eigenfunctions of generalized Laplacians, i.e., symmetric matrices with non-positive off-d…
Magnetic sparseness and Schrödinger operators on graphs
Michel Bonnefont, Sylvain Golénia, Matthias Keller +2
We study magnetic Schrödinger operators on graphs. We extend the notion of sparseness of graphs by including a magnetic quantity called the frustration index. This notion of magnet…
Curvature and higher order Buser inequalities for the graph connection Laplacian
Shiping Liu, Florentin Münch, Norbert Peyerimhoff
We study the eigenvalues of the connection Laplacian on a graph with an orthogonal group or unitary group signature. We establish higher order Buser type inequalities, i.e., we pro…
Frustration index and Cheeger inequalities for discrete and continuous magnetic Laplacians
Carsten Lange, Shiping Liu, Norbert Peyerimhoff +1
We discuss a Cheeger constant as a mixture of the frustration index and the expansion rate, and prove the related Cheeger inequalities and higher order Cheeger inequalities for gra…
Spectral classes of regular, random, and empirical graphs
Jiao Gu, Jürgen Jost, Shiping Liu +1
We define a (pseudo-)distance between graphs based on the spectrum of the normalized Laplacian, which is easy to compute or to estimate numerically. It can therefore serve as a rou…
Eigenvalue ratios of nonnegatively curved graphs
Shiping Liu, Norbert Peyerimhoff
We derive an optimal eigenvalue ratio estimate for finite weighted graphs satisfying the curvature-dimension inequality . This estimate is independent of the size of…
Spectral distances on graphs
Jiao Gu, Bobo Hua, Shiping Liu
By assigning a probability measure via the spectrum of the normalized Laplacian to each graph and using L^p Wasserstein distances between probability measures, we define the corres…
Multi-way dual Cheeger constants and spectral bounds of graphs
Shiping Liu
We introduce a set of multi-way dual Cheeger constants and prove universal higher-order dual Cheeger inequalities for eigenvalues of normalized Laplace operators on weighted finite…