The Petersen graph has no quantum symmetry

TL;DR

This paper proves that the Petersen graph's automorphism group is identical to its quantum automorphism group, confirming it has no quantum symmetry, which resolves a question posed in 2007.

Contribution

The paper establishes that the Petersen graph has no quantum symmetry, showing its quantum automorphism group equals its classical automorphism group.

Findings

The quantum automorphism group of the Petersen graph is the same as its classical automorphism group.

Confirms the Petersen graph has no quantum symmetry.

Resolves a question posed in 2007 about the Petersen graph's quantum symmetry.

Abstract

In 2007, Banica and Bichon asked whether the well-known Petersen graph has quantum symmetry. In this article, we show that the Petersen graph has no quantum symmetry, i.e. the quantum automorphism group of the Petersen graph is its usual automorphism group, the symmetric group $S_5$.