Definition
A biconnected undirected graph is a connected graph that is not broken into disconnected pieces by deleting any single vertex (and its incident edges).
A biconnected directed graph is one such that for any two vertices v and w there are two directed paths from v to w which have no vertices in common other than v and w.
| Vertices | Number of Possibilities |
|---|---|
| 1 | 0 |
| 2 | 1 |
| 3 | 1 |
| 4 | 3 |
| 5 | 10 |
| 6 | 56 |
| 7 | 468 |
| 8 | 7123 |
| 9 | 194066 |
| 10 | 9743542 |
| 11 | 900969091 |
| 12 | 153620333545 |
| 13 | 48432939150704 |
| 14 | 28361824488394169 |
| 15 | 30995890806033380784 |
| 16 | 63501635429109597504951 |
| 17 | 244852079292073376010411280 |
| 18 | 1783160594069429925952824734641 |
| 19 | 24603887051350945867492816663958981 |
Read more about this topic: Biconnected Graph
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