On dihedrants admitting arc-regular group actions
On dihedrants admitting arc-regular group actions
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DOI：
10.1007/s10801-010-0251-7
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发表时间：
2011-05
影响因子：
0.8
通讯作者：
I. Kovács;D. Marušič;M. Muzychuk
中科院分区：
文献类型：
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作者：
I. Kovács;D. Marušič;M. Muzychuk
我们考虑二面体群上的Cayley图Γ，简称二面体，它允许一个正则在Γ弧集上的自同构群G。证明了：如果D2n≤G≤aut(Γ)是2n阶G的正则二面体子群，使得它的任一指标2循环子群都是无核的，则Γ属于这种形式的图族，其中2n=N1⋅⋅⋅nℓm，且数互素.还给出了二面体群上的1-正则二面体和Cayley映射的应用。
We consider Cayley graphsΓover dihedral groups,dihedrantsfor short, which admit an automorphism groupGacting regularly on the arc set ofΓ. We prove that, ifD2n≤G≤Aut(Γ) is a regular dihedral subgroup ofGof order 2nsuch that any of its index 2 cyclic subgroups is core-free inG, thenΓbelongs to the family of graphs of the form, where 2n=n1⋅⋅⋅nℓm, and the numbersniare pairwise coprime. Applications to 1-regular dihedrants and Cayley maps on dihedral groups are also given.