Edge-transitive cyclic regular covers of the Möbius-Kantor graph
Edge-transitive cyclic regular covers of the Möbius-Kantor graph
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DOI：
10.1016/j.ejc.2011.09.034
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发表时间：
2012-02
期刊：
影响因子：
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通讯作者：
Jin-Xin Zhou;Yan-Quan Feng
中科院分区：
文献类型：
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作者：
Jin-Xin Zhou;Yan-Quan Feng
一个连通图X的正则覆盖X称为初等阿贝尔的或循环的，如果它的覆盖变换群分别是初等阿贝尔的或循环的。Malnibu等人研究了其纤维保持群是边传递而不是点传递的Möbius-Kantor图的初等交换正则覆盖。[A. Malniverse，D. Maruši，S. Miklavidian，P. Potočnik，Semisymmetric elementary abelian covers of the Möbius-Kantor graph，Discrete Math.307（2007）2156-2175].本文对纤维保持群是边传递的Möbius-Kantor图的循环正则覆盖进行了分类。作为应用，对每个素数p的16 p阶三次边传递图进行了分类.除112个顶点的Ljubljana图外，所有阶为16 p的三次边传递图都是弧传递的.
A regular cover X˜ of a connected graph X is called elementary abelian or cyclic if its group of covering transformations is elementary abelian or cyclic, respectively. Elementary abelian regular covers of the Möbius–Kantor graph whose fiber preserving groups are edge- but not vertex-transitive were considered by Malnič et al. [A. Malnič, D. Marušič, S. Miklavič, P. Potočnik, Semisymmetric elementary abelian covers of the Möbius–Kantor graph, Discrete Math. 307 (2007) 2156–2175]. In this paper, cyclic regular covers of the Möbius–Kantor graph whose fiber-preserving groups are edge-transitive are classified. As an application, cubic edge-transitive graphs of order 16p for each prime p are classified. Also, it is shown that with the exception of the Ljubljana graph on 112 vertices, all cubic edge-transitive graphs of order 16p are arc-transitive.