Quantum symmetries of Cayley graphs of abelian groups

TL;DR

This paper investigates quantum symmetries in Cayley graphs of abelian groups, providing a method to determine their quantum automorphism groups and applying it to specific graph families.

Contribution

It introduces a general strategy for finding quantum automorphism groups of Cayley graphs of abelian groups and applies it to notable graph classes.

Findings

Quantum automorphism groups of halved cube graphs identified

Quantum symmetries of folded cube graphs characterized

Quantum symmetries of Hamming graphs analyzed

Abstract

We study Cayley graphs of abelian groups from the perspective of quantum symmetries. We develop a general strategy for determining the quantum automorphism groups of such graphs. Applying this procedure, we find the quantum symmetries of the halved cube graph, the folded cube graph and the Hamming graphs.