A332403 Triangle read by rows: T(n,k) is the number of 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

1,5

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.

Links

Table of n, a(n) for n=1..55.

Eric Weisstein's World of Mathematics, Minimal Dominating Set

Example

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;
  ...

Crossrefs

Row sums are A000088.

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

Sequence in context: A307070 A084268 A332405 * A263341 A201198 A349933

Adjacent sequences: A332400 A332401 A332402 * A332404 A332405 A332406

Keyword

nonn,tabl

Author

Andrew Howroyd, Feb 11 2020

Status

approved