A327365 Triangle read by rows where T(n,k) is the number of unlabeled simple graphs covering n vertices with vertex-connectivity >= k.

1, 0, 0, 1, 1, 0, 2, 2, 1, 0, 7, 6, 3, 1, 0, 23, 21, 10, 3, 1, 0, 122, 112, 56, 17, 4, 1, 0, 888, 853, 468, 136, 25, 4, 1, 0, 11302, 11117, 7123, 2388, 384, 39, 5, 1, 0, 262322, 261080, 194066, 80890, 14480, 1051, 59, 5, 1, 0, 11730500, 11716571, 9743542, 5114079, 1211735, 102630, 3211, 87, 6, 1, 0

Offset: 0

Author

Gus Wiseman, Sep 26 2019

Keywords

• nonn
• tabl

Comments

A graph is covering if there are no isolated vertices.

The vertex-connectivity of a graph is the minimum number of vertices that must be removed (along with any incident edges) to obtain a non-connected graph or singleton.

Examples

			Triangle begins:
   1
   0  0
   1  1  0
   2  2  1  0
   7  6  3  1  0
  23 21 10  3  1  0
		

Links

• Gus Wiseman, The graphs counted in row n = 4.

Crossrefs

Column k = 0 is A002494.

Column k = 1 is A001349 (connected graphs), if we assume A001349(0) = A001349(1) = 0.

Column k = 2 is A002218 (2-connected graphs), if we assume A002218(2) = 0.

The non-covering version is A327805, from which this sequence differs only in the k = 0 column.

Extensions

Terms a(21) and beyond from Andrew Howroyd, Dec 26 2020