完全二部图Kp,p的边传递亚循环正则覆盖
Edge-Transitive Metacyclic Regular Covers of the Complete Bipartite Graph Kp,p
DOI: 10.12677/PM.2022.122027, PDF,    国家自然科学基金支持
作者: 黄兆红：鲁东大学数学与统计科学学院，山东 烟台
关键词: 完全二部图；正则覆盖；边传递图；The Complete Bipartite Graph； Regular Cover； Edge-Transitive Graph
摘要: 刻画对称图的正则覆盖是代数图论的基本问题之一，它常常是刻画一般对称图的关键环节。完全二部图作为典型的对称图类，作为正规商图出现在很多传递图类的研究中。本文利用有限群论的技巧和陪集图的相关性质，刻画了2p阶完全二部图的边传递部分亚循环覆盖，并且构造了一类完全二部图的边传递初等交换覆盖。本文的结果将部分亚循环群的覆盖归为幂零群的覆盖问题，将对一般亚循环覆盖的研究起到一定的促进作用。
Abstract: Characterizing regular covers of symmetric graphs is one of the fundamental topics in the field of algebra graph theory, and is often a key step for approaching general symmetric graphs. Complete bipartite graphs, as typical symmetric graphs and normal quotient graphs, appear in many studies of transitive graphs. In this paper, we characterize the edge transitive partial metacyclic covers of complete bipartite graphs of order 2p, and we construct the edge transitive elementary abelian cover of complete bipartite graphs by using the techniques of finite group theory and the related properties of coset graphs. The results of this paper classify the cover of some metacyclic groups as the cover problem of nilpotent groups, which will promote the study of the general metacyclic cover.
文章引用：黄兆红. 完全二部图Kp,p的边传递亚循环正则覆盖[J]. 理论数学, 2022, 12(2): 233-239. https://doi.org/10.12677/PM.2022.122027

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