Some Other Algebraic Properties of Folded Hypercubes

Abstract

We construct explicitly the automorphism group of the folded hypercube $F{Q}_n$ of dimension $n>3$, as a semidirect product of $N$ by $M$, where $N$ is isomorphic to the Abelian group ${\mathbb{Z}}_2^n$, and $M$ is isomorphic to $\mathrm{S}\mathrm{y}\mathrm{m}(n+1)$, the symmetric group of degree $n+1$. Then, we will show that the folded hypercube $F{Q}_n$ is a symmetric graph.