On the Metric Dimension of the Reduced Power Graph of a Finite Group

Let $G$ be a finite group. The reduced power graph of is the undirected whose vertex set $G$, and two distinct vertices $x$ $y$ are adjacent if $\langle x \rangle \subset \langle y \rangle$ or \rangle$. In this paper, we give tight upper lower bounds for metric dimension As applications, compute $\mathcal{P}$-group, cyclic group, dihedral generalized quaternion group odd order.