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Let $S$ be a set of transpositions such that the girth of the transpositiongraph of $S$ is at least 5. It is shown that the automorphism group of theCayley graph of the permutation group $H$ generated by $S$ is the semidirectproduct $R(H) \rtimes \Aut(H,S)$, where $R(H)$ is the right regularrepresentation of $H$ and $\Aut(H,S)$ is the set of automorphisms of $H$ thatfixes $S$ setwise. Furthermore, if the connected components of thetransposition graph of $S$ are isomorphic to each other, then $\Aut(H,S)$ isisomorphic to the automorphism group of the line graph of the transpositiongraph of $S$. This result is a common generalization of previous results byFeng, Ganesan, Harary, Mirafzal, and Zhang and Huang. As another special case,we obtain the automorphism group of the extended cube graph that was proposedas a topology for interconnection networks.

Automorphisms of Cayley graphs generated by transposition sets