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Automorphism group of the derangement graph

By Yun-ping Deng and Xiao-dong Zhang


In this paper, we prove that the full automorphism group of the derangement graph Γn (n ≥ 3) is equal to (R(Sn) ⋊ Inn(Sn)) ⋊ Z2, where R(Sn) and Inn(Sn) are the right regular representation and the inner automorphism group of Sn respectively, and Z2 = 〈ϕ 〉 with the mapping ϕ: σ ϕ = σ −1, ∀ σ ∈ Sn. Moreover, all orbits on the edge set of Γn (n ≥ 3) are determined

Topics: derangement graph, automorphism group, Cayley graph, symmetric
Year: 2013
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