It is known that for any graph $G$ there exists a graph $H$ whose median is isomorphic to $G$: $Med H \cong G$. For any graph $G$. let $f(G)$ denote the minimal number of vertices of a connected graph $H$ satisfying $Med H \cong G$. It is known that if $G$ of diameter two has $n$ vertices and minimal (maximal) degree $\delta (\Delta)$ then $f(G) \geq n+\Delta -\delta$. https://danddcollectiblers.shop/product-category/butter-dishes/