The role of expanders in the spectral geometry of metric graphs

Delio Mugnolo

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arXiv · 2607.14312

The role of expanders in the spectral geometry of metric graphs

Delio Mugnolo

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Abstract

After reviewing combinatorial and spectral definitions of expanders, we use precise lower bounds on Ramanujan graphs to investigate upper bounds -- and, specifically, the lack thereof -- on the eigenvalues of the Laplacian on \emph{metric} graphs in terms of volume, diameter, girth, mean distance, and torsional rigidity, among others.

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Delio Mugnolo. 2026-07-15. The role of expanders in the spectral geometry of metric graphs. https://arxiv.org/abs/2607.14312

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