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A327805
Triangle read by rows where T(n,k) is the number of unlabeled simple graphs with n vertices and vertex-connectivity >= k.
4
1, 1, 0, 2, 1, 0, 4, 2, 1, 0, 11, 6, 3, 1, 0, 34, 21, 10, 3, 1, 0, 156, 112, 56, 17, 4, 1, 0, 1044, 853, 468, 136, 25, 4, 1, 0, 12346, 11117, 7123, 2388, 384, 39, 5, 1, 0, 274668, 261080, 194066, 80890, 14480, 1051, 59, 5, 1, 0, 12005168, 11716571, 9743542, 5114079, 1211735, 102630, 3211, 87, 6, 1, 0
OFFSET
0,4
COMMENTS
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. Note that this means a single node has vertex-connectivity 0.
FORMULA
T(n,k) = Sum_{j=k..n} A259862(n,j).
EXAMPLE
Triangle begins:
1
1 0
2 1 0
4 2 1 0
11 6 3 1 0
34 21 10 3 1 0
CROSSREFS
Row-wise partial sums of A259862.
The labeled version is A327363.
The covering case is A327365, from which this sequence differs only in the k = 0 column.
Column k = 0 is A000088 (graphs).
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 triangle for vertex-connectivity exactly k is A259862.
Sequence in context: A290222 A327549 A293808 * A276689 A091453 A062173
KEYWORD
nonn,tabl
AUTHOR
Gus Wiseman, Sep 26 2019
EXTENSIONS
Terms a(21) and beyond from Andrew Howroyd, Dec 26 2020
STATUS
approved