K5,5− 5K2覆盖变换群为S4的正则覆盖的分类
2-Arc-Transitive Regular Covers of K5,5 − 5K2 with the Covering Transformation Group S4
DOI: 10.12677/PM.2023.1310306, PDF,   
作者: 李群苗：北方工业大学理学院，北京
关键词: 弧–传递图；覆盖图；提升；Arc-Transitive Graph； Covering Graph； Lifting
摘要: 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。
Abstract: 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.
文章引用：李群苗. K5,5− 5K2覆盖变换群为S4的正则覆盖的分类[J]. 理论数学, 2023, 13(10): 2978-2984. https://doi.org/10.12677/PM.2023.1310306

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