具有边界的图上组合 p-Laplacian first Dirichlet 特征值的 Faber-Krahn 不等式
组合数学
2026-03-31 v2
摘要
本文推导了具有固定顶点数或固定边数且连通的具有边界的图上组合 p-Laplacian first Dirichlet 特征值的尖锐 Faber-Krahn 不等式。更具体地说，我们证明了在 p>1 时，顶点数为 n 或边数为 n 的具有边界的连通图的 first p-Dirichlet 特征值的最小值仅在 tadpole 图 上 achieved。
引用
@article{arxiv.2603.20814,
title = {Faber-Krahn inequalities for first Dirichlet eigenvalues of combinatorial $p$-Laplacian on graphs with boundary},
author = {Wankai He and Chengjie Yu},
journal= {arXiv preprint arXiv:2603.20814},
year = {2026}
}
备注
Statements of the main results are strengthen, the title has been changed to make it more specified