阶为三的次幂倍奇素数幂的边本原图

Edge-Primitive Graphs of Order Three to the Power Times an Odd Prime Power

称一个图是边本原的,如果其全自同构群在其边集上的作用是本原的。通过Li的研究成果,我们可以得到包含子群的指数为三的次幂倍奇素数幂的本原置换群,并且将连通的非平凡边本原图分为了三种情形。本文我们考虑顶点本原的情形,刻画阶为三的次幂倍奇素数幂乘积的边本原图。最后我们可以构造出五个新的边本原图例子。

A graph is called edge-primitive, if its automorphism group acts primitively on its edge set. Through Li’s research findings, we can obtain the primitive permutation group with a subgroup of index three to the power times an odd prime power and divide the connected non-trivial edge-primitive graphs into three cases. In this paper, edge-primitive graphs of order three to the power times an odd prime power are characterized by considering the case of vertex-primitive. Finally, we can construct five new examples of edge-primitive graphs.