In this paper we study the Cayley graph $\mathrm{Cay}(S_n,T)$ of the symmetric group $S_n$ generated by a set of transpositions $T$. We show that for $n\geq 5$ the Cayley graph is normal. As a corollary, we show that its automorphism group is a direct product of $S_n$ and the automorphism group of the transposition graph associated to $T$. This provides an affirmative answer to a conjecture raised by Ganesan in arXiv:1703.08109, showing that $\mathrm{Cay}(S_n,T)$ is normal if and only if the transposition graph is not $C_4$ or $K_n$.

翻译：本文研究由对换集$T$生成的对换群$S_n$的Cayley图$\mathrm{Cay}(S_n,T)$。我们证明当$n\geq 5$时，该Cayley图是正规的。作为推论，我们证明其自同构群是$S_n$与$T$所关联的对换图的自同构群的直积。这为Ganesan在arXiv:1703.08109中提出的猜想提供了肯定性回答，表明$\mathrm{Cay}(S_n,T)$是正规的当且仅当对换图不是$C_4$或$K_n$。