2.3.3. Measurments in a graph

The eccentricity of a vertex v is the number .

The radius is the minimum eccentricity among the vertices of G, while the diameter of G is the maximum eccentricity.

A central vertex in a graph of radius rad G is one whose eccentricity is rad G i.e. a vertex v such that .

Theorem 2.11. For every connected graph G, .

Proof. The left hand side is trivial. To prove the right hand side we choose u and v such that . Let w be a central vertex of G.

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