Chuanyuan Ge

activity

20222026

collaborators

9 papers

math.CO2026

New bounds for equiangular lines and Balla's conjecture

Chuanyuan Ge, Shiping Liu

Let $N_{α} (d)$ denote the maximum number of equiangular lines in $R^{d}$ with common angle $arccos (α)$ . Balla conjectured that, if the spectral radius order $κ_{\frac{1-α}{2α…

math.CO2025

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 $arccos (1/5)$ . This conjecture was previously re…

math.CO2025

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…

math.CO2025

Equiangular lines via nodal domains

Chuanyuan Ge, Shiping Liu

For given $Δ > 0$ and $0 < λ < 3/ 2$ , we show that the maximum multiplicity that $λ$ can appear as the second largest eigenvalue of a connected graph with maximum degree at most $Δ…

math.NA2025

Computing the $p$ -Laplacian eigenpairs of signed graphs

Chuanyuan Ge, Ouyuan Qin

As a nonlinear extension of the graph Laplacian, the graph $p$ -Laplacian has various applications in many fields. Due to the nonlinearity, it is very difficult to compute the eigen…

math.CO2024

Spectral bounds of multi-way Cheeger constants via cyclomatic number

Chuanyuan Ge

As a non-trivial extension of the celebrated Cheeger inequality, the higher-order Cheeger inequalities for graphs due to Lee, Oveis Gharan and Trevisan provide for each $k$ an uppe…

math.SP2023

New graph invariants based on $p$ -Laplacian eigenvalues

Chuanyuan Ge, Shiping Liu, Dong Zhang

We present monotonicity inequalities for certain functions involving eigenvalues of $p$ -Laplacians on signed graphs with respect to $p$ . Inspired by such monotonicity, we propose n…

math.SP2022

Nodal domain theorems for $p$ -Laplacians on signed graphs

Chuanyuan Ge, Shiping Liu, Dong Zhang

We establish various nodal domain theorems for $p$ -Laplacians on signed graphs, which unify most of the existing results on nodal domains of graph $p$ -Laplacians and arbitrary symm…

math.SP2022

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…

New bounds for equiangular lines and Balla's conjecture

A new proof of the Lemmens-Seidel conjecture

On finiteness of spectral radius order

Equiangular lines via nodal domains

Computing the p-Laplacian eigenpairs of signed graphs

Spectral bounds of multi-way Cheeger constants via cyclomatic number

New graph invariants based on p-Laplacian eigenvalues

Nodal domain theorems for p-Laplacians on signed graphs

Symmetric Matrices, Signed Graphs, and Nodal Domain Theorems

Computing the $p$ -Laplacian eigenpairs of signed graphs

New graph invariants based on $p$ -Laplacian eigenvalues

Nodal domain theorems for $p$ -Laplacians on signed graphs