阶为八倍奇素数的边本原图

Edge-Primitive Graphs of Order Eight Times an Odd Prime

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四倍奇素数和八倍奇素数的本原置换群,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和二部本原的情形,刻画阶为八倍奇素数的边本原图。

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 four times an odd prime and eight times an odd prime, and divide the connected non-trivial edge-primitive graphs into three cases. In this paper, edge-primitive graphs of order eight times an odd prime are characterized by considering the case of vertex-primitive and vertex-biprimitive.