论文标题
生成nilpotent组生成图的连通性
Connectivity of generating graphs of nilpotent groups
论文作者
论文摘要
令$ g $为$ 2 $生成的群体。 $γ（g）$的生成图是其顶点是$ g $的元素，如果$ g = \ langle g，h \ rangle $，则两个顶点$ g $和$ h $相邻。该图编码跨$ g $的生成对分布的组合结构。在本文中，我们研究了几种与$γ（g）$的连接性相关的自然图理论特性，在$ g $是有限的nilpotent群体的情况下。例如，我们证明，如果$ g $是nilpotent，则通过删除其隔离顶点从$γ（g）$获得的图形获得最大连接，如果$ | g | \ geq 3 $，也是哈密顿人。我们提出了几个问题。
Let $G$ be $2$-generated group. The generating graph of $Γ(G)$ is the graph whose vertices are the elements of $G$ and where two vertices $g$ and $h$ are adjacent if $G=\langle g,h\rangle$. This graph encodes the combinatorial structure of the distribution of generating pairs across $G$. In this paper we study several natural graph theoretic properties related to the connectedness of $Γ(G)$ in the case where $G$ is a finite nilpotent group. For example, we prove that if $G$ is nilpotent, then the graph obtained from $Γ(G)$ by removing its isolated vertices is maximally connected and, if $|G| \geq 3$, also Hamiltonian. We pose several questions.
