Affiliation:
1. Institute of Photogrammetry and Remote Sensing, Karlsruhe Institute of Technology , Englerstr. 7, 76131 Karlsruhe, Germany
Abstract
For a finite graph, a spectral curve is constructed as the zero set of a two-variate polynomial with integer coefficients coming from p-adic diffusion on the graph. It is shown that certain spectral curves can distinguish non-isomorphic pairs of isospectral graphs, and can even reconstruct the graph. This allows the graph reconstruction from the spectrum of the associated p-adic Laplacian operator. As an application to p-adic geometry, it is shown that the reduction graph of a Mumford curve and the product reduction graph of a p-adic analytic torus can be recovered from the spectrum of such operators.
Funder
Deutsche Forschungsgemeinschaft
Subject
Mathematical Physics,Statistical and Nonlinear Physics
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