奇数阶完全图的因子分解与对称群

On the Factorization of Isomorph in Odd Complete Graph

F.Harary在[1]中提出如下一个未解决问题:那些有限置换群是完全图同构分解的因子对称群?对于n>1。构造了2n+1阶完全图G的n个不同的同构分解Ge=G1∪G2∪…∪Gn,其中G1是2n个点的路的第e对对称点和另1个点连接得到的图。证明了G的同构分解的因子对称群是n阶循环群。

F. Harary [1] posed an unresolved problem as follows： which finite permutation groups are the factor symmetric groups of isomorphic partition for complete graph？ For any n〉0, a factorization of K2n＋1 is gained： G^e=G1∪G2∪…∪Gn. It is proved that the cyclic group of order n is the symmetric group of the partition.