9.9 If G is a connected graph, a centre of G is a vertex v with the property that the maximum of the distances between v and the other vertices of G is as small as possible. By succes- sively removing...

Extracted text: 9.9 If G is a connected graph, a centre of G is a vertex v with the property that the maximum of the distances between v and the other vertices of G is as small as possible. By succes- sively removing end-vertices, prove that every tree has either one centre or two adjacent centres. Give an example of a tree of each type with 7 vertices.