  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. To obtain the proper enhanced
power graph, we consider the induced subgraph on the set G\D, where D
represents the set of dominating vertices in the enhanced power graph. In this
paper, we aim to determine the strong domination number of the proper enhanced
power graphs of finite nilpotent groups.
