Year: 2024
Type: article
Abstract: 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 $n\geq 5$ 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 $C_4$ or $K_n$.
DOI: 10.37236/12771
Authors: Dion Gijswijt, Frank De Meijer
Institution: Delft University of Technology
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4402271745