论文标题
与有限组相关的增强功率图的某些属性
Certain properties of the enhanced power graph associated with a finite group
论文作者
论文摘要
有限的组$ g $的增强功率图，由$ \ Mathcal {p} _e（g）$表示，是一个简单的无向图，其顶点集为$ g $，而两个不同的顶点$ x，y $如果$ x，y \ in \ langle z \ langle z \ rangle z \ rangle $ for n $ z \ in g $ in g $ in g $。在本文中，我们确定所有有限组，以便$ \ Mathcal {p} _e（g）$的最低度和顶点连接相等。同样，我们对所有（适当）增强功率图的（适当）非常规规则的组进行了分类。此外，还获得了与某些Nilpotent组相关的增强功率图的顶点连接。最后，我们获得了$ \ Mathcal {p} _e（g）$的Wiener索引的下限和上限，其中$ g $是一个nilpotent组。达到这些边界的有限尼尔植物组也是特征的。
The enhanced power graph of a finite group $G$, denoted by $\mathcal{P}_E(G)$, is the simple undirected graph whose vertex set is $G$ and two distinct vertices $x, y$ are adjacent if $x, y \in \langle z \rangle$ for some $z \in G$. In this article, we determine all finite groups such that the minimum degree and the vertex connectivity of $\mathcal{P}_E(G)$ are equal. Also, we classify all groups whose (proper) enhanced power graphs are strongly regular. Further, the vertex connectivity of the enhanced power graphs associated to some nilpotent groups is obtained. Finally, we obtain a lower bound and an upper bound for the Wiener index of $\mathcal{P}_E(G)$, where $G$ is a nilpotent group. The finite nilpotent groups attaining these bounds are also characterized.
