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A327805
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Triangle read by rows where T(n,k) is the number of unlabeled simple graphs with n vertices and vertex-connectivity >= k.
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4
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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
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OFFSET
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0,4
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COMMENTS
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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.
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LINKS
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FORMULA
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T(n,k) = Sum_{j=k..n} A259862(n,j).
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EXAMPLE
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Triangle begins:
1
1 0
2 1 0
4 2 1 0
11 6 3 1 0
34 21 10 3 1 0
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CROSSREFS
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The covering case is A327365, from which this sequence differs only in the k = 0 column.
Column k = 2 is A002218 (2-connected graphs), if we assume A002218(2) = 0.
The triangle for vertex-connectivity exactly k is A259862.
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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