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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.
Gijswijt et al. (Thu,) studied this question.
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