K_5,5− 5K₂覆盖变换群为S₄的正则覆盖的分类

2-Arc-Transitive Regular Covers of K_5,5 − 5K₂ with the Covering Transformation Group S₄

研究对称图的正则覆盖是代数图论的重要课题。为了更深入了解对称图的性质与分类,利用群论的基本知识,本文分类了K5,5 − 5K2的正则覆盖,其中覆盖变换群同构于S4,且保纤维自同构群的作用是2-弧传递的。最后,证明了满足条件的覆盖图是不存在的。

Studying the regular covering of symmetric graphs is an important topic in algebraic graph theory. In order to have a deeper understanding of the properties and classification of symmetric graphs, using the basic knowledge of group theory, in this paper, a classification is achieved for all the regular covers of K5,5 − 5K2 whose covering transformation group is isomorphic to S4 and whose fiber-preserving automorphism group acts 2-arc-transitively. It is proved that the covering graph that satisfies the conditions does not exist.