Geodesic
Automorphism groups of Cayley graphs generated by general transposition sets
Dion Gijswijt1 ; Frank de Meijer2
1Delft University of Technology
2TU Delft
The electronic journal of combinatorics, Tome 31 (2024) no. 3
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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
Classification : 05C25, 20B30
Mots-clés : transposition graph, symmetric group

Dion Gijswijt  1   ; Frank de Meijer  2

1 Delft University of Technology
2 TU Delft 
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     author = {Dion Gijswijt and Frank de Meijer},
     title = {Automorphism groups of {Cayley} graphs generated by general transposition sets},
     journal = {The electronic journal of combinatorics},
     year = {2024},
     volume = {31},
     number = {3},
     doi = {10.37236/12771},
     zbl = {1548.05159},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/12771/}
}
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Dion Gijswijt; Frank de Meijer. Automorphism groups of Cayley graphs generated by general transposition sets. The electronic journal of combinatorics, Tome 31 (2024) no. 3. doi: 10.37236/12771

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