Finite s-Arc Transitive Cayley graphs and Flag-Transitive Projective Planes
Finite s-Arc Transitive Cayley graphs and Flag-Transitive Projective Planes
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DOI：
10.1090/s0002-9939-04-07549-5
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发表时间：
2004-07
期刊：
影响因子：
--
通讯作者：
Caiheng Li
中科院分区：
文献类型：
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作者：
Caiheng Li
本文给出了s > 2的有限s-弧传递Cayley图的一个刻画。特别地，证明了对于任意给定的整数k，k > 3，k <$= 7，存在有限的s-传递Cayley图集（可能为空），使得所有k度的s-传递Cayley图都是它们的正规覆盖，其中s ∈ {3，4，5，7}.这表明s ≥ 3的s-弧传递Cayley图是非常罕见的。然而，它被证明存在4-弧传递凯莱图的每一个允许的价（一个素数幂加1）。然后证明了旗传递非Deserkesian射影平面的存在性等价于二面体群的弧传递正规Cayley图的存在性。
In this paper, a characterisation is given of finite s-arc transitive Cayley graphs with s > 2. In particular, it is shown that, for any given integer k with k > 3 and k ¬= 7, there exists a finite set (maybe empty) of s-transitive Cayley graphs with s ∈ {3, 4, 5, 7} such that all s-transitive Cayley graphs of valency k are their normal covers. This indicates that s-arc transitive Cayley graphs with s ≥ 3 are very rare. However, it is proved that there exist 4-arc transitive Cayley graphs for each admissible valency (a prime power plus one). It is then shown that the existence of a flag-transitive non-Desarguesian projective plane is equivalent to the existence of a very special arc transitive normal Cayley graph of a dihedral group.