阶为三的次幂倍奇素数幂的边本原图
Edge-Primitive Graphs of Order Three to the Power Times an Odd Prime Power
DOI: 10.12677/PM.2022.126100, PDF,    科研立项经费支持
作者: 赖子峰：云南财经大学，统计与数学学院，云南 昆明
关键词: 边本原图；本原置换群；几乎单型；Edge-Primitive Graph； Primitive Permutation Group； Almost Simple Type
摘要: 称一个图是边本原的，如果其全自同构群在其边集上的作用是本原的。通过Li的研究成果，我们可以得到包含子群的指数为三的次幂倍奇素数幂的本原置换群，并且将连通的非平凡边本原图分为了三种情形。本文我们考虑顶点本原的情形，刻画阶为三的次幂倍奇素数幂乘积的边本原图。最后我们可以构造出五个新的边本原图例子。
Abstract: A graph is called edge-primitive, if its automorphism group acts primitively on its edge set. Through Li’s research findings, we can obtain the primitive permutation group with a subgroup of index three to the power times an odd prime power and divide the connected non-trivial edge-primitive graphs into three cases. In this paper, edge-primitive graphs of order three to the power times an odd prime power are characterized by considering the case of vertex-primitive. Finally, we can construct five new examples of edge-primitive graphs.
文章引用：赖子峰. 阶为三的次幂倍奇素数幂的边本原图[J]. 理论数学, 2022, 12(6): 911-918. https://doi.org/10.12677/PM.2022.126100

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