阶为8p2的5度对称图
Pentavalent Symmetric Graphs of Order Eight Times a Prime Square
DOI: 10.12677/PM.2020.1012141, PDF,    国家自然科学基金支持
作者: 杨婷婷, 王 蒙：云南财经大学统计与数学学院，云南 昆明
关键词: 对称图；拟本原；二部拟本原；单群；Symmetric Graph； Quasiprimitive； Bi-Quasiprimitive； Simple Group
摘要: 如果图的自同构群Aut(Г)在图的弧集上是可传递的，则称图是对称的(或弧传递的)。设Г是一个连通图，G ≤ Aut(Г)，如果G作用在VΓ上是拟本原或顶点二部拟本原的，则称Γ是G-基图。在本文中，我们将分类阶为8p2的5度对称G-基图，其中p为奇素数。证明了自同构群在图的顶点集上拟本原时存在一个图。当自同构群在图的顶点集上二部拟本原时，存在两个图。
Abstract: A graph is symmetric (or arc-transitive) if its automorphism group Aut(Г) is transitive on the arc set of the graph. Let Г be a connected graph and G ≤ Aut(Г). Then Γ is called a G-basic graph, if G is quasiprimitive or bi-quasiprimitive on VΓ. In this paper, we give a classification of connected pentavalent symmetric graphs of order 8p2, where p is an odd prime. It is proved that there is a graph of the automorphism group is quasiprimitive on the vertex set, while there are two graphs exist in the case of the automorphism group is biquasiprimitive on the vertex set.
文章引用：杨婷婷, 王蒙. 阶为8p2的5度对称图[J]. 理论数学, 2020, 10(12): 1183-1189. https://doi.org/10.12677/PM.2020.1012141

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