论文标题
在奇数秩序的阿贝尔组上，凯利图的稳定性
Stability of Cayley graphs on abelian groups of odd order
论文作者
论文摘要
令$ x $是一个连接的cayley图，上面是一组奇数订单，这样$ x $的两个截然不同的顶点都具有完全相同的邻居。我们表明，直接产品$ x \ times k_2 $（也称为$ x $的“规范双盖”）只有明显的自动形态（即，来自其因子$ x $ and $ k_2 $的自动形态的自动形态）。这意味着$ x $是“稳定”。证明是简短而基本的。直接产品的理论意味着$ k_2 $可以用更普遍的连接图家族的成员代替。
Let $X$ be a connected Cayley graph on an abelian group of odd order, such that no two distinct vertices of $X$ have exactly the same neighbours. We show that the direct product $X \times K_2$ (also called the "canonical double cover" of $X$) has only the obvious automorphisms (namely, the ones that come from automorphisms of its factors $X$ and $K_2$). This means that $X$ is "stable". The proof is short and elementary. The theory of direct products implies that $K_2$ can be replaced with members of a much more general family of connected graphs.
