A332404 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with irredundance number k.

1, 1, 1, 2, 1, 1, 4, 5, 1, 1, 11, 16, 5, 1, 1, 34, 94, 21, 5, 1, 1, 156, 710, 150, 21, 5, 1, 1, 1044, 9419, 1691, 164, 21, 5, 1, 1, 12346, 221979, 38207, 1944, 164, 21, 5, 1, 1, 274668, 9907071, 1773452, 47802, 1983, 164, 21, 5, 1, 1

Offset: 1

Author

Andrew Howroyd, Feb 11 2020

Keywords

• nonn
• tabl

Comments

The irredundance number of a graph is the minimum size of a maximal irredundant set.

For any graph the following relation holds:

irredundance number (this sequence)

<= domination number (A263284)

<= independent domination number (A332402)

<= independence number (A263341)

<= upper domination number (A332403)

<= upper irredundance number (A332405).

Examples

			Triangle begins:
       1;
       1,       1;
       2,       1,       1;
       4,       5,       1,     1;
      11,      16,       5,     1,    1;
      34,      94,      21,     5,    1,   1;
     156,     710,     150,    21,    5,   1,  1;
    1044,    9419,    1691,   164,   21,   5,  1, 1;
   12346,  221979,   38207,  1944,  164,  21,  5, 1, 1;
  274668, 9907071, 1773452, 47802, 1983, 164, 21, 5, 1, 1;
  ...
		

Links

• Eric Weisstein's World of Mathematics, Maximal Irredundant Set

Crossrefs

Row sums are A000088.

Column k=1 is A000088(n-1).

Cf. A263284, A263341, A332402, A332403, A332404, A332405.

Formula

T(n,k) = T(n-1,k-1) for 2*(k-1) >= n.