On the spectrum of unitary finite-Euclidean graphs

TL;DR

This paper investigates the spectral properties of unitary finite-Euclidean graphs constructed over Z_d^n, demonstrating their integrality under specific conditions related to the dimension and parity.

Contribution

It establishes the integrality of the spectra of these graphs when n is odd or d is even, extending understanding of their algebraic structure.

Findings

Graphs are integral when n is odd.

Graphs are integral when d is even.

Provides conditions for spectral integrality.

Abstract

We consider unitary graphs attached to Z_d^n using an analogue of the Euclidean distance. These graphs are shown to be integral when n is odd or the dimension d is even.