Q 33.Consider the tree given below .

Using the property of eccentricity of a vertex, find every vertex that is the centre of the given tree.
(A) d & h
(B) c & k
(C) g, b, c, h, i, m
(D) c & h
Answer(d)
Given a graph, the eccentricity of a vertex v is defined as the greatest distance from v to any other vertex. A center (also: centroid)of a graph is a vertex with minimal eccentricity. A graph can have an arbitrary number of centers. If we take e as the center then e to n it will cover 5 edges.
E to l 5 edges.
E to J 5 edges.
If we make B as the center than it will have to cover max 4 edges to reach the remotest node.
Similarly to D and G. to cover max 4 edges to reach every remotest node.
C and H will have to to cover max 3 edges to reach every remotest node.
I,K and M will have to to cover max 4 edges to reach every remotest node.
J,L,N will have to to cover max 5edges to reach every remotest node.
Hence it is optimal to choose C and H as the centre of tree. It has two centres.