Let $T = (V, E)$ be a tree, and let $v \in V$ be any vertex of $T$.
- The $\text{eccentricity}$ of $v$ is the maximum distance from $v$ to any other vertex in $T$.
- The $\text{centre } C$ of $T$ is the set of vertices which have minimum eccentricity among all vertices in $T$.
- The $\text{weight of }v$ is the number of vertices in the largest subtree of $v$.
- The $\text{centroid }$ $C$ of $T$ is the set of vertices with minimum weight among all vertices in $T$.
Construct a tree $T$ that has disjoint centre and centroid, each having two vertices (i.e. $C \cap \mathcal{C} = \not{O}$ and $|C| = |\mathcal{C}| = 2)$.