Hypercubes are determined by their distance spectra

TL;DR

This paper proves that the structure of a d-dimensional hypercube can be uniquely identified by the eigenvalues of its distance matrix, establishing a spectral characterization.

Contribution

It introduces a spectral characterization of hypercubes, showing they are uniquely determined by their distance spectra, a novel result in graph theory.

Findings

Hypercubes are uniquely determined by their distance spectra

Distance spectra can distinguish hypercubes from other graphs

Spectral methods can identify hypercube structures

Abstract

We show that the d-cube is determined by the spectrum of its distance matrix.