A331422 Triangle T(n, k) of the number of connected graphs of order n with cutting number k >= 0.

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

Offset: 1

Author

Sean A. Irvine, Jan 16 2020

Keywords

• nonn
• tabf

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.

Examples

			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.
		

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.

Crossrefs

Cf. A331238 (trees), A001349 (row sums), A002218 (first column).