论文标题
循环器的规范双盖
Canonical double covers of circulants
论文作者
论文摘要
图$ x $的规范双盖$ b（x）$是$ x $和$ k_2 $的直接产品。如果$ aut（b（x））\ cong aut（x）\ times \ times \ mathbb {z} _2 $，则$ x $称为稳定；否则$ x $称为不稳定。如果连接连接，一个不稳定的图形在不稳定的情况下是不稳定的，非彼比特和不同的顶点具有不同的邻域。循环液是循环组上的Cayley图。秦等人。在[J.组合。理论ser。 B 136（2019），154-169]，没有奇数的非平稳循环器。在本文中，我们证明了这个猜想。
The canonical double cover $B(X)$ of a graph $X$ is the direct product of $X$ and $K_2$. If $Aut(B(X)) \cong Aut(X) \times \mathbb{Z}_2$ then $X$ is called stable; otherwise $X$ is called unstable. An unstable graph is nontrivially unstable if it is connected, non-bipartite and distinct vertices have different neighborhoods. Circulant is a Cayley graph on a cyclic group. Qin et al. conjectured in [J. Combin. Theory Ser. B 136 (2019), 154-169] that there are no nontrivialy unstable circulants of odd order. In this paper we prove this conjecture.
