This work studies edge-transitive bi-circulants of order $2n$ with ${\mathbb{Z}}_n$ being a Hall subgroup of the full automorphism groups. The automorphism groups of such graphs are completely determined. As an application, a classification is given of bipartite edge-transitive bi-circulants of order $2n$ with valency less than the smallest prime divisors of $n$. This also leads to a new construction of an infinite family of arc-regular bi-circulants.

中文翻译：

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有限的边缘传递双环流

这项工作研究有序的边缘传递双环流 $\mathrm{2个}ñ$ 和 ${\mathbb{ž}}_{ñ}$是完全同构组的Hall子组。这样的图的自同构群是完全确定的。作为应用，给出了二阶边沿传递双环流的分类$\mathrm{2个}ñ$ 化合价小于的最小主除数 $ñ$。这也导致了无限大的弧形双圆弧族的新构造。