On isospectral metric graphs
Pavel Kurasov, Jacob Muller
TL;DR
This paper introduces a novel class of isospectral metric graphs, constructed by gluing subgraphs with special Steklov map properties, revealing a link between isospectrality and Steklov eigenvalue degeneracy.
Contribution
It presents a new method for creating isospectral graphs using Steklov maps, expanding understanding of spectral properties in metric and discrete graphs.
Findings
New class of isospectral graphs with specific construction method
Isospectrality linked to Steklov eigenvalue degeneracy
Applicable to both normalized Laplacian and differential Laplacian
Abstract
A new class of isospectral graphs is presented. These graphs are isospectral with respect to both the normalised Laplacian on the discrete graph and the standard differential Laplacian on the corresponding metric graph. The new class of graphs is obtained by gluing together subgraphs with the Steklov maps possessing special properties. It turns out that isospectrality is related to the degeneracy of the Steklov eigenvalues.
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Taxonomy
TopicsAdvanced Computational Techniques in Science and Engineering · Graph theory and applications · Scientific Research and Studies