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.

中文翻译：

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有限三次图允许在顶点上最多三个轨道的自同构循环群

电压图的理论已经成为研究图的标准工具，允许自同构的半正则群。我们引入了循环广义电压图的概念，以将这一理论的范围扩展到允许可能不是半正则的自同构循环群的图。我们使用这个新工具对所有承认最多具有三个顶点轨道的自同构循环群的立方图进行分类，并且我们表征了这些类中的每一个的顶点传递性。特别是，我们证明了一个三次顶点传递图，它允许一个循环群的自同构在顶点上最多三个轨道，要么属于 5 个无限家族中的一个，要么与众所周知的 Tutte-Coxeter 图同构。