Automorphism Groups of the Pancake Graphs

TL;DR

This paper investigates the properties of pancake graphs, proving their super- and hyper-connectivity, and fully characterizes their automorphism groups, revealing their symmetry and regular representation of the symmetric group.

Contribution

It provides the first complete determination of the automorphism group of pancake graphs, establishing their symmetry properties and connectivity features.

Findings

Pancake graphs are super-connected and hyper-connected.

For n ≥ 5, pancake graphs are graphical regular representations of S_n.

The automorphism group of P_n is fully characterized.

Abstract

It is well-known that the pancake graphs are widely used as models for interconnection networks \cite{Akers}. In this paper, some properties of the pancake graphs are investigated. We first prove that the pancake graph, denoted by $P_n (n\geq 4),$ is super-connected and hyper-connected. Further, we study the symmetry of $P_n$ and completely determine its full automorphism group,which shows that $P_n (n\geq 5)$ is a graphical regular representation of $S_n.$