Show how to generalize the graph in Figure 4.4 to an arbitrary number of states M ≥ 3 with one cycle of M nodes and one of M 1 nodes. For M = 4, let node 1 be the node not in the cycle of M 1 nodes....

Show how to generalize the graph in Figure 4.4 to an arbitrary number of states M ≥ 3 with one cycle of M nodes and one of M 1 nodes. For M = 4, let node 1 be the node not in the cycle of M 1 nodes. List the set of states accessible from node 1 in n steps for each n ≤ 12 and show that the bound in Theorem 4.2.4 is met with equality. Explain why the same result holds for all larger M.