Automorphism Groups of the Pancake Graphs

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 $P_n(n\ge 4),$ is super-connected and hyper-connected. Further, we study the symmetry of $P_n$ and completely determine its full automorphism group,which shows that $P_n(n\ge 5)$ is a graphical regular representation of $S_n\mathrm{.}$