D_n上的Cayley图的同构因子分解

ISOMORPHIC FACTORIZATION OF CAYLEY GRAPH ON D_n

证明了素数度的阶为2n 的二面体群 D_n 上的 Cayley 图在 n 为奇,或 n 为2~k,或特征集满足一定条件下是有理的。同时也证明了三度二面体群上的 Cayley 图是有理的。

The following result is proved:cayley graph with prime degree on a dihedralgroup D_n of order 2n is rational if n is odd or 2~k,or any condition is satisfied for characteris-tic set.It is also proved that Cayley graph with 3 degree on a dihedral group is rational.