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Automorphism Groups of Cayley Graphs Generated by General Transposition Sets

Journal Article (2024)
Author(s)

Dion Gijswijt (TU Delft - Discrete Mathematics and Optimization)

Frank Meijer (TU Delft - Discrete Mathematics and Optimization)

Research Group
Discrete Mathematics and Optimization
DOI related publication
https://doi.org/10.37236/12771
More Info
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Publication Year
2024
Language
English
Research Group
Discrete Mathematics and Optimization
Issue number
3
Volume number
31
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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.