Automorphism Groups of Cayley Graphs Generated by General Transposition Sets

In this paper we study the Cayley graph Cay(S_n, T) of the symmetric group S_n generated by a set of transpositions T. We show that for n ≥ 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 A. Ganesan, Cayley graphs and symmetric interconnection networks, showing that Cay(S_n, T) is normal if and only if the transposition graph is not C₄ or K_n.