One can hear a discrete rectangular torus

TL;DR

This paper proves that two discrete rectangular tori are isospectral if and only if they are structurally identical, establishing a unique spectral characterization for these geometric objects.

Contribution

It provides a complete characterization of isospectrality for discrete rectangular tori, showing spectral data determines their isomorphism.

Findings

Two discrete rectangular tori are isospectral iff they are isomorphic.

Spectral data uniquely identifies discrete rectangular tori.

The result establishes a spectral rigidity for these structures.

Abstract

In the present paper, we prove that two discrete rectangular tori are isospectral if and only if they are isomorphic.