Define the geodesic (short path) distance between two nodes as the minimum number of
hops from one node to the other. Define the diameter of a network as the maximum geodesic
distance among all the pairs of two nodes. Define the degree of a node as the number of
links connected to that node.
1. If the diameter of a network with 100 nodes is 1, what is the minimum number of links
in this network?
2. If the diameter of a network with 100 nodes is 2, what is the minimum number of links
in this network?
3. For a network of 100 nodes, if the degree of every node is at most 2, what is the
minimum diameter of that network?
4. For a network of 100 nodes, if the degree of every node is at most 3, is it possible that
the diameter of this network is not greater than 5?
