A332403 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with upper domination number k.

1, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 13, 15, 4, 1, 1, 36, 83, 30, 5, 1, 1, 101, 582, 302, 51, 6, 1, 1, 365, 6024, 5025, 843, 80, 7, 1, 1, 1518, 99497, 144370, 27160, 1996, 117, 8, 1, 1, 8002, 2706069, 7441209, 1733211, 112291, 4211, 164, 9, 1

Offset: 1

Author

Andrew Howroyd, Feb 11 2020

Keywords

• nonn
• tabl

Comments

First differs from A263341 in row 6.

The upper domination number of a graph is the maximum size of a minimal dominating set (a set that is both dominating and irredundant). For any graph it is greater than or equal to the independence number (A263341) and less than or equal to the upper irredundance number (A332405). The number of graphs where it is strictly greater than is given in A332407.

Examples

			Triangle begins:
  1;
  1,    1;
  1,    2,       1;
  1,    6,       3,       1;
  1,   13,      15,       4,       1;
  1,   36,      83,      30,       5,      1;
  1,  101,     582,     302,      51,      6,    1;
  1,  365,    6024,    5025,     843,     80,    7,   1;
  1, 1518,   99497,  144370,   27160,   1996,  117,   8, 1;
  1, 8002, 2706069, 7441209, 1733211, 112291, 4211, 164, 9, 1;
  ...
		

Links

• Eric Weisstein's World of Mathematics, Minimal Dominating Set

Crossrefs

Row sums are A000088.

Cf. A263284, A263341, A332402, A332404, A332405, A332407.