基柱为PSL(3,4)的几乎单群的边本原图

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

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.

Let Г be a graph. An element G of Sym（V） is called an automorphism of F. If G preserves the adjacen-cy ofГ . The set of all the automorphism of Г forms a subgroup of Sym （ V）, called the full automorphism of thegroup of Г, and is denoted as Aut（Г）. Specially, if G acts primitively on EF, then F 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 sim- ple group with socle PSL（3,4）.