  In this paper, we consider the monoid $DPW_n$ of all partial isometries of a
wheel graph $W_n$ with $n+1$ vertices. Our main objective is to determine the
rank of $DPW_n$. In the process, we also compute the ranks of three notable
subsemigroups of $DPW_n$. We also describe Green's relations of $DPW_n$ and of
its three considered subsemigroups.
