基柱为PSL(3,4)的几乎单群的边本原图

设Γ是一个图,若群G作用在图Γ的顶点集上保持边的连接关系,则称群G是图Γ的自同构群.进一步,若G作用在图Γ的边集上是本原的,则称图Γ是G-边本原图.边本原图是一类重要的对称图.通过构造陪集图的方法来研究边本原图,并给出基柱为PSL(3,4)的几乎单群的边本原图的分类.

Edge-primitive graphs for an almost simple group with socle PSL( 3,4)

Let Γ be a graph. An element G of Sym( V) is called an automorphism of Γ. If G preserves the adjacency of Γ. The set of all the automorphism of Γ forms a subgroup of Sym( V),called the full automorphism of the group of Γ,and is denoted as Aut( Γ). Specially,if G acts primitively on EΓ,then Γ is said to be G- edge-primitive. The edge- primitive graphs are an important kind of symmetric graphs. This paper studies the edge-primitive graphs via the construction of coset graphs and classifies all G- edge- primitive graphs of the almost simple group with socle PSL( 3,4).