Eigenvalues of the discrete p-Laplacian via graph surgery

2025/09/08 by Gregory Berkolaiko, Matthias Hofmann, Berkolaiko, Gregory +1 · 1 citation
Computer Science · #05C22 #05C50 #35J10 #35J92 #35R02 #81Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics #Topological and Geometric Data Analysis

paper · pdf · doi:10.48550/arxiv.2509.06686

openalex publication_date 2025/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We develop a Hellmann--Feynman type perturbation theory for the discrete signed p-Laplacian and apply it to a parametrized perturbation by edge cuts. We show that the eigenvalues of the signed p-Laplacian can be characterized as citical values of the parameter-dependent eigenvalues of a simpler graph.

Citations

• Nodal domain theorems for p-Laplacians on signed graphs
• The Cheeger Cut and Cheeger Problem in Metric Graphs
• Nodal domain count for the generalized graph p-Laplacian
• The self-consistent field iteration for p-spectral clustering
• A nodal domain theorem and a higher-order Cheeger inequality for the\n graph p-Laplacian

Cited by

• Combinatorial Courant-Fischer-Weyl Minimax Principle on Cheeger k-constants of Weighted Forests

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