第二小阶数的点本原1/2-弧传递图

Vertex-Primitive 1/2 -Arc-Transitive Graph with Second Small Order

通过研究群PSL(3,3)在二维射影空间PV(2 ,3)中极大独立点集之集合上的本原作用的次轨道结构 ,构造了一个阶数为 2 34,度数为 48,自同构群为Aut(PSL(3,) )的点本原 12 弧传递图 ,从而发现了第二小阶数的点本原 12 弧传递图 .

A graph is called 12 -arc -transitive if it is vertex and edge transitive but not arc transitive.In this paper,the action of group PSL(3,3) on the set of maximal sets of independent points in the projective sapce PG(2,3) is considered,resulting in a vertex -prmitive 12 -arc -transitive with order 234,valency 48 and automorphism group Aut( PSL (3,3)).In fact,this graph is the vertex -primitive 12 -arc -transitive graph of second small order.