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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 $|C| = |\mathcal{C}| = 2)$.

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