Assume we have simple connected graph with vertices v1,v2,..vn and with edges e1, e2,...,ek. Now for any pair of vertices there will be at least one path connecting them. For each pair of vertices, find the shortest possible path that connects them. The longest of these pairwise shortest paths is called the diameter of the graph.
a. Draw a graph of six vertices with a diameter of 5.
b. Draw a graph of 6 vertices with a diameter of 1.
c. Prove that a graph of n vertices with a Hamiltonian cycle must have a diameter no larger than n/2 (if n is even) or (n-1)/2 if n is odd.