Automorphism Groups of Cayley Graphs Generated by General Transposition Sets

In this paper we study the Cayley graph Cay(S_n,T) of thesymmetric group S_n generated by a set of transpositions T. We show thatfor n≥ 5 the Cayley graph is normal. As a corollary, we show that itsautomorphism group is a direct product of S_n and the automorphism group ofthe transposition graph associated to T. This provides an affirmative answerto a conjecture raised by Ganesan in arXiv:1703.08109, showing thatCay(S_n,T) is normal if and only if the transposition graph is notC_4 or K_n.