s-弧传递可解Cayley图  

s-arc-transitive solvable Cayley graphs

作　　者：李才恒 潘江敏 张颖楠 Caiheng Li;Jiangmin Pan;Yingnan Zhang

机构地区：[1]南方科技大学数学系,深圳518055 [2]云南财经大学统计与数学学院,昆明650221

出　　处：《中国科学：数学》2024年第7期1029-1044,共16页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11931005和11961076)资助项目。

摘　　要：本文刻画了度数大于等于3的连通s-弧传递可解Cayley图(s≥3).本文证明了这些图都是4类具体的图的正规覆盖,特别地,证明了s的上确界为4,并指出了一个4-弧传递可解Cayley图的无穷类.In this paper,we characterize the connected s-arc-transitive solvable Cayley graphs with s≥3 and valency of at least three.We prove that such graphs are the normal covers of four specific families of graphs.In particular,we show that the sharp upper bound on s is 4,and we point out an infinite family of 4-arc-transitive solvable Cayley graphs.

关 键 词：上确界 s-弧传递图 CAYLEY图 可解群 

分 类 号：O157.5[理学—数学]