

A331422


Triangle T(n, k) of the number of connected graphs of order n with cutting number k >= 0.


2



1, 1, 1, 1, 3, 0, 2, 1, 10, 0, 0, 5, 3, 2, 1, 56, 0, 0, 0, 29, 0, 13, 8, 3, 2, 1, 468, 0, 0, 0, 0, 219, 0, 0, 63, 69, 0, 16, 12, 3, 2, 1, 7123, 0, 0, 0, 0, 0, 2706, 0, 0, 0, 502, 263, 300, 0, 85, 80, 24, 16, 12, 3, 2, 1, 194066, 0, 0, 0, 0, 0, 0, 52879, 0, 0, 0, 0, 6191, 3197, 0, 2148, 861, 632, 319, 352, 132, 160, 80, 24, 21, 12, 3, 2, 1
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OFFSET

1,5


COMMENTS

The cutting number of a node v in a graph G is the number of pairs of nodes {u,w} of G such that u!=v, w!=v, and every path from u to w contains v. The cutting number of a connected graph, is the maximum cutting number of any node in the graph.


LINKS

Sean A. Irvine, Rows n = 1..12 flattened
Sean A. Irvine, Java program (github)
Simon Mukwembi and Senelani Dorothy HoveMusekwa, On bounds for the cutting number of a graph, Indian J. Pure Appl. Math., 43 (2012), 637649.


EXAMPLE

The triangle begins:
1;
1;
1, 1;
3, 0, 2, 1;
10, 0, 0, 5, 3, 2, 1;
56, 0, 0, 0, 29, 0, 13, 8, 3, 2, 1;
468, 0, 0, 0, 0, 219, 0, 0, 63, 69, 0, 16, 12, 3, 2, 1;
...
The length of row n is 1 + (n1)*(n2)/2.


CROSSREFS

Cf. A331238 (trees), A001349 (row sums), A002218 (first column).
Sequence in context: A295041 A127913 A135991 * A279631 A102003 A176314
Adjacent sequences: A331419 A331420 A331421 * A331423 A331424 A331425


KEYWORD

nonn,tabf


AUTHOR

Sean A. Irvine, Jan 16 2020


STATUS

approved



