How to prove the enhanced power graph of dihedral groups?

Question

According to Aalipour et al. (2016), they defined the enhanced power graph of group $G$ as a simple undirected graph where the vertices are all elements of $G$ and two vertices, $x$ and $y$, are adjacent if $\langle x,y \rangle$ is belong to the same cyclic subgroup of $G$. Let $G$ be the dihedral group of order $2n$. I know that the only possibility is that the rotation elements of $G$ are always cyclic and form a clique, but for the set of the reflection element of $G$, it is just connected to the $e$. How can we write the proper proof of it?