The Automorphism Group of the Petersen Graph is Isomorphic to $S_5$

TL;DR

This paper proves that the automorphism group of the Petersen Graph is isomorphic to the symmetric group on five elements, providing a clear algebraic characterization of its symmetries.

Contribution

It establishes the isomorphism between the Petersen Graph's automorphism group and S_5, offering a new perspective on its symmetry structure.

Findings

Automorphism group is isomorphic to S_5

Vertices represented by 3-element subsets of {1,2,3,4,5}

Adjacency based on one-element intersection

Abstract

The automorphism group of the Petersen Graph is shown to be isomorphic to the symmetric group on 5 elements. The image represents the Petersen Graph with the ten 3-element subsets of $\{1, 2, 3, 4, 5\}$ as vertices. Two vertices are adjacent when they have precisely one element in common.