标题： 玫瑰窗图的稳定性 显示英文标题

标题： Stability of Rose Window graphs

摘要： 一个图$\Gamma$被称为稳定，如果对于直积$\Gamma\times\mathbf{K}_2$，${\rm Aut}(\Gamma \times \mathbf{K}_2)$与${\rm Aut}(\Gamma) \times \mathbb{Z}_2$同构；否则，它被称为不稳定。 一个不稳定的图被称为非平凡不稳定，当它不是二部图且没有两个顶点具有相同的邻域。 Wilson 描述了九类不稳定的玫瑰窗图，并猜想这些包含所有非平凡不稳定的玫瑰窗图（2008）。 在本文中，我们证明该猜想是正确的。 显示英文摘要

摘要： A graph $\Gamma$ is said to be stable if for the direct product $\Gamma\times\mathbf{K}_2$, ${\rm Aut}(\Gamma \times \mathbf{K}_2)$ is isomorphic to ${\rm Aut}(\Gamma) \times \mathbb{Z}_2$; otherwise, it is called unstable. An unstable graph is called non-trivially unstable when it is not bipartite and no two vertices have the same neighborhood. Wilson described nine families of unstable Rose Window graphs and conjectured that these contain all non-trivially unstable Rose Window graphs (2008). In this paper we show that the conjecture is true.