This paper deals with the vertex connectivity of enhanced power graphs of finite groups. We classify all abelian groups G such that the vertex connectivity of enhanced power graph of G is 1. We derive an upper bound for the vertex connectivity of the enhanced power graph of any general abelian group G. Also we completely characterize all abelian groups G, such that the proper enhanced power graph is connected. Moreover, we study some special class of non-abelian groups G such that the proper enhanced power graph is connected and we find their vertex connectivity.

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关于有限群增强功率图的连通性

本文讨论了有限群增强幂图的顶点连通性。我们分类所有阿贝尔群G ^，使得增强的功率曲线图的顶点连接ģ是1推导的上界的任何一般阿贝尔群的增强的功率图的顶点连接ģ。同样，我们完全表征了所有阿贝尔群G，从而连接了适当的增强功率图。此外，我们研究了一些特殊类别的非阿贝尔群G，使得适当的增强功率图得以连接，并且找到了它们的顶点连通性。