K6,6 − 6K2覆盖变换群为S4的正则覆盖的分类
2-Arc-Transitive Regular Covers of K6,6 − 6K2 with the Covering Transformation Group S4
DOI: 10.12677/pm.2025.158224, PDF,   
作者: 严 红：北方工业大学理学院，北京
关键词: 2-弧传递；正则覆盖；提升；Arc-transitive； Regular Covering； Lifting
摘要: 对称图的正则覆盖是图论于代数的重要研究内容，在多个领域有广泛的应用。本文对K6,6 − 6K2的正则覆盖进行研究，其中覆盖变换群是S4，且保纤维自同构群的作用是2-弧传递的，应用群扩张的理论证明了满足条件的覆盖图是不存在的。
Abstract: The regular coverings of symmetric graphs are important research contents in graph theory and algebra, which have been widely applied in many fields. This paper studies the regular coverings of K6,6 − 6K2, where the covering transformation group is S4, and the action of the fiber-preserving automorphism group is 2-arc-transitive. By using the theory of group extensions, it is proved that there is no covering graph satisfying the conditions.
文章引用：严红. K6,6 − 6K2覆盖变换群为S4的正则覆盖的分类[J]. 理论数学, 2025, 15(8): 98-103. https://doi.org/10.12677/pm.2025.158224

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