ℓp阶三度边传递图 献给刘桂真教授80寿辰  

Trivalent edge-transitive graphs of orderℓp

作　　者：周进鑫[1] 冯衍全 Jinxin Zhou;Yanquan Feng

机构地区：[1]北京交通大学数学与统计学院,北京100044

出　　处：《中国科学：数学》2024年第11期1943-1960,共18页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11731002,12071023和12161141005)资助项目。

摘　　要：如果一个图的自同构群在它的边集合上作用传递,则称这个图是边传递的.本文给出ℓp阶三度连通边传递图的刻画,其中p是素数,ℓ(0<ℓ<p)为整数.作为应用,首先,在0<ℓ654且p为素数时,给出ℓp阶三度连通半对称图的分类;其次证明当0<ℓ≤100且p为素数时,所有ℓp阶三度连通边传递图都是已知的.A graph is edge-transitive if its automorphism group acts transitively on its edges.In this paper,we give a characterization of connected edge-transitive trivalent graphs of orderℓp,where p is a prime andℓ(0<ℓ<p)is an integer.Applying this characterization,we first give a classification of connected semisymmetric trivalent graphs of orderℓp with 0<ℓ654 and p a prime,and then we show that all connected edge-transitive trivalent graphs of orderℓp with 0<ℓ≤100 and p a prime are known.

关 键 词：边传递 半对称图 双CAYLEY图 

分 类 号：O157.5[理学—数学]