A259862 Triangle read by rows: T(n,k) = number of unlabeled graphs with n nodes and connectivity exactly k (n>=1, 0<=k<=n-1).
1, 1, 1, 2, 1, 1, 5, 3, 2, 1, 13, 11, 7, 2, 1, 44, 56, 39, 13, 3, 1, 191, 385, 332, 111, 21, 3, 1, 1229, 3994, 4735, 2004, 345, 34, 4, 1, 13588, 67014, 113176, 66410, 13429, 992, 54, 4, 1, 288597, 1973029, 4629463, 3902344, 1109105, 99419, 3124, 81, 5, 1, 12297299, 105731474, 327695586, 388624106, 162318088, 21500415, 820956, 9813, 121, 5, 1
Offset: 1
Examples
Triangle begins:
1;
1, 1;
2, 1, 1;
5, 3, 2, 1;
13, 11, 7, 2, 1;
44, 56, 39, 13, 3, 1;
191, 385, 332, 111, 21, 3, 1;
1229, 3994, 4735, 2004, 345, 34, 4, 1;
13588, 67014, 113176, 66410, 13429, 992, 54, 4, 1;
288597, 1973029, 4629463, 3902344, 1109105, 99419, 3124, 81, 5, 1;
12297299,105731474,327695586,388624106,162318088,21500415,820956,9813,121,5,1;
...
Links
- Georg Grasegger, Table of n, a(n) for n = 1..78
- Brendan McKay, confusion over k-connected graphs, posting to Sequence Fans Mailing List, Jul 08 2015.
- Jens M. Schmidt, Combinatorial Data
- Gus Wiseman, The graphs counted by row n = 5 (isolated vertices not shown).
Crossrefs
Columns k=0..10 (up to initial nonzero terms) are A000719, A052442, A052443, A052444, A052445, A324234, A324235, A324088, A324089, A324090, A324091.
Row sums are A000088.
Number of graphs with connectivity at least k for k=1..10 are A001349, A002218, A006290, A086216, A086217, A324240, A324092, A324093, A324094, A324095.
The labeled version is A327334.
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