论文标题
易于检测图形规则表示的组
Groups for which it is easy to detect graphical regular representations
论文作者
论文摘要
我们说，有限的G组正在“ drr检测”，如果对于G的每个子集，Cayley Digraph Cay（g，s）是一种定期的定期代表（即，其自动形态群体定期在其角度上起作用），或者在其顶点集合），或者有一个非无事的g phi the n n n n n n n n n n n n n n n n nil nil nil nil nil nil nil s = s） p组，但对于每个奇数p，两个循环级别P的花圈产物并不是DRR检测。我们还表明，如果g和h是允许进行挖掘常规表示的非平凡组，而gcd（| g |，| h |）= 1或h不是drr检测，则直接乘积g x h不是drr检测。其中一些结果还具有用于图形规则表示形式的类似物。
We say that a finite group G is "DRR-detecting" if, for every subset S of G, either the Cayley digraph Cay(G,S) is a digraphical regular representation (that is, its automorphism group acts regularly on its vertex set) or there is a nontrivial group automorphism phi of G such that phi(S) = S. We show that every nilpotent DRR-detecting group is a p-group, but that the wreath product of two cyclic groups of order p is not DRR-detecting, for every odd prime p. We also show that if G and H are nontrivial groups that admit a digraphical regular representation and either gcd(|G|,|H|) = 1, or H is not DRR-detecting, then the direct product G x H is not DRR-detecting. Some of these results also have analogues for graphical regular representations.
