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arXiv · 2412.02200

On Spectra of Metric Tree Graphs

Tyler Chamberlain
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Abstract

The secular manifold $\Sigma_G$ and its singularities are intimately related to the spectra of metric graphs $(G,\ell)$. In this paper, we present a complete description of the singular locus for tree graphs, and confirm that it agrees with a conjecture of Colin de Verdi\`ere. We also discuss numerous applications toward studying the behavior of metric tree graphs.

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Tyler Chamberlain. 2024-12-03. On Spectra of Metric Tree Graphs. https://arxiv.org/abs/2412.02200

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