论文标题
关于阿贝尔群体上cayley图的两部分定期表示的存在和枚举
On the existence and the enumeration of bipartite regular representations of Cayley graphs over abelian groups
论文作者
论文摘要
在本文中，我们对阿贝尔群体上两方面的Cayley Digraphs和Cayley图的渐近枚举感兴趣。让$ a $为ABELIAN集团，让$ b $为$ a^i = a^{ - 1} $定义的$ a $的自动形态，对于$中的每个$ a \。 Cayley Graph $ \ cay（a，s）$据说如果$ \ aut（\ cay（a，s））= \ langle a，i \ rangle $，则尽可能小。在本文中，我们表明，除了两个无限家庭外，阿贝尔群体上几乎所有的两分之一的cayley图具有尽可能小的自动形态组。我们还调查了两部分Cayley Digraphs的类似问题。
In this paper we are interested in the asymptotic enumeration of bipartite Cayley digraphs and Cayley graphs over abelian groups. Let $A$ be an abelian group and let $ι$ be the automorphism of $A$ defined by $a^ι=a^{-1}$, for every $a\in A$. A Cayley graph $\Cay(A, S)$ is said to have an automorphism group as small as possible if $\Aut(\Cay(A,S)) = \langle A,ι\rangle$. In this paper, we show that, except for two infinite families, almost all bipartite Cayley graphs on abelian groups have automorphism group as small as possible. We also investigate the analogous question for bipartite Cayley digraphs.
