Illustrations of the maximum state degrees and long-range connections.

Green states indicate open states while blue indicates all other states A) A representative topology with a labeled state that has five possible connections to other states. By cutting out the red portion (containing the extraneous state and connection), the indicated state then has a degree of four. B) A representative model graph that has cycle length of six. Removal of the indicated red dashed connection breaks the cycle. The resulting topology has a maximum cycle length of four C) A representative 8-state topology that meets the maximum state and long-range connections restrictions illustrated in A & B and is included in the final count in Fig 1E (i.e. is an example of the 72,489 unique rooted topologies).

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