Computer Networks Homework # 1

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?

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