Geodesic
Automorphism group of the derangement graph
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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In this paper, we prove that the full automorphism group of the derangement graph $\Gamma_n$ ($n\geq3$) is equal to $(R(S_n)\rtimes\hbox{Inn} (S_n))\rtimes Z_2$, where $R(S_n)$ and $\hbox{Inn} (S_n)$ are the right regular representation and the inner automorphism group of $S_n$ respectively, and $Z_2=\langle\varphi\rangle$ with the mapping $\varphi:$ $\sigma^{\varphi}=\sigma^{-1},\,\forall\,\sigma\in S_n.$ Moreover, all orbits on the edge set of $\Gamma_n$ ($n\geq3$) are determined.
DOI : 10.37236/685
Classification : 05C25, 05C69
Mots-clés : derangement graph, automorphism group, Cayley graph, symmetric group 
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     author = {Yun-Ping Deng and Xiao-Dong Zhang},
     title = {Automorphism group of the derangement graph},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/685},
     zbl = {1230.05151},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/685/}
}
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Yun-Ping Deng; Xiao-Dong Zhang. Automorphism group of the derangement graph. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/685

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