Symmetry groups of some perfect 1-factorizations of complete graphs
Symmetry groups of some perfect 1-factorizations of complete graphs
复制标题
完全图的一些完美 1 因式分解的对称群
DOI：
10.1016/0012-365x(77)90126-1
复制
发表时间：
1977
期刊：
影响因子：
--
通讯作者：
B. A. Anderson
中科院分区：
文献类型：
--
作者：
B. A. Anderson
在图、格和有限拓扑的研究中出现了以下问题。是否存在K2 m在2n个点上的完全图的1-因子分解，使得每对不同的1-因子的并集是一个Hamilton回路？在本文中，我们注意到在K2 m1 <$n <$5上，直到重新标号，只有一个所需类型的1-因子分解。在K12上，只要有奇素数p，q> 3使得p+ 1= 2 q，至少有两个不同的1-因子分解。这些结果是通过计算对称群得到的。所得到的对称群是最大阶的Frobenius群（即锐2-传递群）和这些群与阶为2的群的直积。
The following problem has arisen in the study of graphs, lattices and finite topologies. Is there a 1-factorization of K 2m the complete graph on 2n points, such that the union of every pair of distinct 1-factors is a hamiltonian circuit? In this paper it is noted that on K 2m 1⪕ n⪕ 5, there is, up to relabelling, only one 1-factorization of the required type. On K 12 and whenever there are odd primes p, q> 3 such that p+ 1= 2q, there are at least two different such 1-factorizations. These results are obtained by computing symmetry groups. The symmetry groups obtained are Frobenius groups of maximal order (ie, sharply 2-transitive groups) and direct products of these groups with the group of order 2.