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arXiv · 2509.06686

Eigenvalues of the discrete p-Laplacian via graph surgery

Gregory Berkolaiko·Matthias Hofmann
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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.

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Gregory Berkolaiko, Matthias Hofmann. 2025-09-08. Eigenvalues of the discrete p-Laplacian via graph surgery. https://arxiv.org/abs/2509.06686

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