2r阶循环群的最小图

The Smallest Graph with Cyclic Group of Order 2r

构造出自同构群是2r阶循环群且具有2r+6个顶点的边数最少的图并证明这样的图只有一个.

Let α(n) be the least number of points for which a graph has automorphism group isomorphic to c(n), the cyclic group of order n. Let β(n) represent the least number of lines a graph can have if it has α(n) points and automorphism group isomorphic to c(n). And that there is only one graph for c(2r) with α(2r) points and β(2r) lines is proved.