Quantum automorphism group of the lexicographic product of finite regular graphs

TL;DR

This paper explores the quantum automorphism group of the lexicographic product of finite regular graphs, extending classical automorphism results into the quantum domain.

Contribution

It introduces a quantum generalization of Sabidussi's theorem for the automorphism group of lexicographic product graphs.

Findings

Established a quantum analogue of Sabidussi's structure theorem

Characterized the quantum automorphism group for the product of finite regular graphs

Extended classical graph automorphism concepts into quantum symmetry context

Abstract

We study the quantum automorphism group of the lexicographic product of two finite regular graphs, providing a quantum generalization of Sabidussi's structure theorem on the automorphism group of such a graph.