容许对称群的有限2-弧传递图  

Finite 2-Arc Transitive Graphs with Symmetric Groups

作　　者：张莉 王改霞[1] ZHANG Li;WANG Gaixia(School of Microelectronics and Data Science,Anhui University of Technology,Maanshan Anhui,243002,China)

机构地区：[1]安徽工业大学微电子与数据科学学院,安徽马鞍山243002

出　　处：《新疆大学学报（自然科学版）（中英文）》2023年第5期543-549,共7页Journal of Xinjiang University(Natural Science Edition in Chinese and English)

基　　金：supported by National Natural Science Foundation of the People’s Republic of China“On the symmetries and local properties of graphs with square-free order”(11601005);Anhui Provincial Science Fund for Excellent Young Scholars“On the symmetries of edge-primitive graphs with square-free order”(gxyq2020011).

摘　　要：如果图Γ至少有一个2-弧且其自同构群在点集和2-弧集合上是传递的,则称该图为2-弧传递图.设G是基柱为交错群Ac(其中c≥5)的几乎单群,利用陪集图概念构造无平方因子阶的(G,2)-弧传递图.再通过分析自同构群和其点稳定子群的子群链结构,给出了该类图的分类.The graphis said to be 2-arc-transitive if it has at least one 2-arc and Aut()is transitive on both the vertices and 2-arcs of.Let G be an almost simple group with soc(G)=Ac for c≥5,we use the concept of coset graph to construct the graphs with square-free order and(G,2)-arc-transitive.Then by analyzing the subgroup chain structures between vertex-stabilizer subgroups and their automorphism groups,a classification of the(G,2)-arc transitive graphs of square-free order was given.

关 键 词：对称图 无平方因子阶 2-弧传递图 自同构群 

分 类 号：O157.5[理学—数学]