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.
.