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{\bf Yun-Ping Deng and Xiao-Dong Zhang}
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{\bf Automorphism Group of the Derangement Graph}
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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 
$(R(S_n)\rtimes\hbox{\rm Inn} (S_n))\rtimes Z_2$,  
where $R(S_n)$ and $\hbox{\rm Inn} (S_n)$ 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.

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