A263294 Triangle read by rows: T(n,k) is the number of unlabeled simple graphs with n vertices and treewidth k.

1, 1, 1, 1, 2, 1, 1, 5, 4, 1, 1, 9, 17, 6, 1, 1, 19, 72, 53, 10, 1, 1, 36, 323, 501, 168, 14, 1, 1, 75, 1639, 5889, 4163, 557, 21, 1, 1, 152, 9203, 81786, 138923, 42596, 1977, 29, 1

Offset: 1

Author

Christian Stump, Oct 13 2015

Keywords

• nonn
• tabl
• more

Comments

A graph without edges has treewidth 0, any other forest has treewidth 1, any other series parallel graph has treewidth 2. - Martin Rubey, May 10 2023

Examples

			Triangle begins:
  1;
  1,   1;
  1,   2,    1;
  1,   5,    4,     1;
  1,   9,   17,     6,      1;
  1,  19,   72,    53,     10,     1;
  1,  36,  323,   501,    168,    14,    1;
  1,  75, 1639,  5889,   4163,   557,   21,  1;
  1, 152, 9203, 81786, 138923, 42596, 1977, 29, 1;
  ...
		

Links

• FindStat - Combinatorial Statistic Finder, The treewidth of a graph.
• Wikipedia, Treewidth

Crossrefs

Columns k=2..3 are A362908, A362907.

Partial row sums include A000012, A005195, A000041.

Row sums are A000088.

T(n,n-2) = A000065(n).

Extensions

Corrected and extended by Martin Rubey, May 10 2023