3^r阶循环群的最小图

The Smallest Graph with Cyclic Group of Order 3^r

设α(n)是自同构群与n阶循环群C(n)同构的图的最小顶点数,该文构造出群为C(3r)的具有α(3r)个顶点的边数最少的图,并证明了这样的图是唯一的.

Let α（n） be the least number of points for which a graph has its automorphism group isormorphic to C（n）,the cyclic group of order n.Let β（3r） represent the least number of lines a graph can have if it has α（n） points and the automorphismgroup isormorphic to C（n）.We prove that,as far as C（3r） is concerned,there is only one graph with points and β（3r）（=3r＋1＋6） lines.