有限幂零群的增强幂图的顶点连通度的精确枚举
An exact enumeration of vertex connectivity of the enhanced power graphs of finite nilpotent groups
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AI总结：
本文针对有限幂零群的增强幂图，精确确定了其顶点连通度，给出了完整的枚举结果。
AI中文摘要：
群 $G$ 的增强幂图是一个以 $G$ 为顶点集的图，其中两个不同顶点 $x$ 和 $y$ 相邻当且仅当存在 $G$ 中元素 $w$，使得 $x$ 和 $y$ 都是 $w$ 的幂。本文确定了任意有限幂零群的增强幂图的顶点连通度。
英文摘要：
The enhanced power graph of a group $G$ is a graph with vertex set $G,$ where two distinct vertices $x$ and $y$ are adjacent if and only if there exists an element $w$ in $G$ such that both $x$ and $y$ are powers of $w.$ In this paper, we determine the vertex connectivity of the enhanced power graph of any finite nilpotent group.
