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