14pq阶的五度对称图
Pentavalent Symmetric Graphs of Order 14pq
DOI: 10.12677/AAM.2024.132072, PDF,   
作者: 赵路清, 凌 波*：云南民族大学数学与计算机科学学院，云南 昆明
关键词: 对称图；自同构群；正规商图；Symmetric Graph； Automorphism Group； Normal Quotient Graph
摘要: 称一个图为对称图，如果它的自同构群在这个图的弧集上是传递的。丁素云、凌波、娄本功和潘江敏教授2016年在文献(Graphs and Combinatorics, 32, 2355-2366, 2016)中证明了：无平方因子阶的五度对称图要么同构于图CDn,k、C390 、C2926，要么这类图的全自同构群为PSL(2,p)和PGL(2,p)。本文的主要工作是在假定一个五度图的阶为14pq时，完全确定其图全自同构群为PSL(2,p)和PGL(2,p)对应的对称图，其中q>p>5为素数。
Abstract: A graph is said to be symmetric if its automorphism group acts transitively on its arcs. In 2016, Ding Suyun, Ling Bo, Lou Bengong and professors Pan Jiangmin published a paper in the (Graphs and Combinatorics, 32, 2355-2366, 2016), proved that: Arc-transitive pentavalent graphs of square-free order are either isomorphic to graphs CDn,k、C390 、C2926 , or the full automorphism group of such graphs is PSL(2,p) and PGL(2,p) . The main work of this paper is to completely determine that the full automorphism group of a pentavalent graph as PSL(2,p) and PGL(2,p) corresponds to a symmetric graph when the order of the graph is assumed to be 14pq, where q>p>5 are primes.
文章引用：赵路清, 凌波. 14pq阶的五度对称图[J]. 应用数学进展, 2024, 13(2): 738-743. https://doi.org/10.12677/AAM.2024.132072

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