圈C_n的自同构群

The automorphism group of Cycle C_n

一个图的自同构群通常反映了该图的对称性,讨论一个图的自同构群构造是代数图论中的基本问题之一。直观上可以看出,圈Cn的自同构群是2n阶的,但对于其具体构造目前还没有形式化的证明。作者基于群作用的思想,利用群的轨道方程对此问题研究,得出Cn的自同构群是一个二面体群的结论。通过严格的推证,表明该结论是可靠的。

The automorphism group usually reflects the symmetry of a graph. To determine the construction of the group of a graph is one of the focus problems in algebraic graph theory. Intuitionally, the authors think that the order of Aut（Cn） is 2. But there is never a machinery proof for now. In this paper, the problem will be solved by the orbit equation based on the action of a group on the vertex set of cycle Cn. Therefore, the authors will know that the automorphism group of a cycle on n vertices is isomorphic to a dihedral group.