Automorphism Groups of Cayley Graphs Generated by General Transposition Sets
Dion Gijswijt (TU Delft - Discrete Mathematics and Optimization)
F.J.J. de Meijer (TU Delft - Discrete Mathematics and Optimization)
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Abstract
In this paper we study the Cayley graph Cay(Sn, T) of the symmetric group Sn 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 Sn 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(Sn, T) is normal if and only if the transposition graph is not C4 or Kn.
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