A graph Γ is called a bi-circulant if it admits a cyclic group as a group of automorphisms acting semiregularly on the vertices of Γ with two orbits. The characterization of tetravalent edgetransitive bi-circulants was given in several recent papers. In this paper, a classification is given of connected tetravalent vertex-transitive bi-circulants of order twice an odd integer.

中文翻译：

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关于四价顶点传递双循环

如果图Γ允许一个循环群作为半同规作用于具有两个轨道的Γ的顶点的一组自同构，则它称为双圆。最近的几篇论文中对四价边缘传递性双环化剂进行了表征。在本文中，给出了连接的四阶顶点传递双环流的分类，其阶数是奇整数的两倍。