论文标题
有限的立方图，在顶点上最多有三个轨道的自动形态循环群
Finite cubic graphs admitting an cyclic group of automorphisms with at most three orbits on vertices
论文作者
论文摘要
电压图的理论已成为研究图的标准工具，该工具承认了半毛体的自动形态。我们介绍了循环通用电压图的概念，以扩展该理论的范围，以示出可能不是半晶状体的循环的自动形态群。我们使用此新工具来对所有具有最多三个顶点孔的自动形态的循环型自动形态进行分类，我们对每个类别的certextransitivity进行了表征。特别是，我们表明了一个立方顶点传递图，该图构成了一个自动形态的循环群，顶点上最多有三个轨道属于5个无限家族之一，或者是熟悉的Tutte-Coxeter图的同构。
The theory of voltage graphs has become a standard tool in the study graphs admitting a semiregular group of automorphisms. We introduce the notion of a cyclic generalised voltage graph to extend the scope of this theory to graphs admitting a cyclic group of automorphism that may not be semiregular. We use this new tool to classify all cubic graphs admitting a cyclic group of automorphisms with at most three vertex-orbits and we characterise vertextransitivity for each of these classes. In particular, we show that a cubic vertex-transitive graph admitting a cyclic group of automorphisms with at most three orbits on vertices either belongs to one of 5 infinite families or is isomorphic to the well-know Tutte-Coxeter graph.
