论文标题
对称图的封面和伪跨
Covers and pseudocovers of symmetric graphs
论文作者
论文摘要
我们介绍了对称图的伪造概念，这是封面的对应物。迄今为止，唯一已知的对称图的伪封闭者是普拉格（Praeger），周（Zhou）和十年前的头号作者给出的，这似乎是技术性的，很难扩展以获取更多示例。在本文中，我们介绍了对称图的对称扩展器为伪越野跨的标准，然后将其应用于产生各种伪越野遗传的示例，包括（1）具有单个例外，每个Praeger-XU的图是一个伪造的伪越野镜； （2）每个连接的四接对称图，具有$ 32 $的尺寸的顶点稳定器，均具有连接的伪越过。
We introduce the concept of pseudocover, which is a counterpart of cover, for symmetric graphs. The only known example of pseudocovers of symmetric graphs so far was given by Praeger, Zhou and the first-named author a decade ago, which seems technical and hard to extend to obtain more examples. In this paper, we present a criterion for a symmetric extender of a symmetric graph to be a pseudocover, and then apply it to produce various examples of pseudocovers, including (1) with a single exception, each Praeger-Xu's graph is a pseudocover of a wreath graph; (2) each connected tetravalent symmetric graph with vertex stabilizer of size divisible by $32$ has connected pseudocovers.
