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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 (list; graph; refs; listen; history; text; internal format)
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 Hove-Musekwa, On bounds for the cutting number of a graph, Indian J. Pure Appl. Math., 43 (2012), 637-649.

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 + (n-1)*(n-2)/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

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Last modified December 2 23:09 EST 2020. Contains 338898 sequences. (Running on oeis4.)