The enhanced power graph \({\mathcal {P}}_E(G)\) of a group G is a simple undirected graph with the vertex set G and two vertices are adjacent if they belong to the same cyclic subgroup of G. In this paper, we have obtained the metric dimension and the resolving polynomial of the enhanced power graph of the non-abelian group of order p3, where p is an odd prime. We also study the coloring and detour distance properties of the graph \({\mathcal {P}}_E(G)\) .
