A263284 Triangle read by rows: T(n,k) is the number of unlabeled simple graphs on n vertices with domination number k.

1, 1, 1, 2, 1, 1, 4, 5, 1, 1, 11, 16, 5, 1, 1, 34, 94, 21, 5, 1, 1, 156, 708, 152, 21, 5, 1, 1, 1044, 9384, 1724, 166, 21, 5, 1, 1, 12346, 221135, 38996, 1997, 166, 21, 5, 1, 1, 274668, 9877969, 1800340, 49961, 2036, 166, 21, 5, 1, 1

Offset: 1

Author

Christian Stump, Oct 13 2015

Keywords

• nonn
• tabl
• more

Comments

The domination number of a graph is given by the minimum size of a dominating set of vertices. A dominating set of vertices is a subset of the vertex set of such that every vertex is either in this subset or adjacent to an element of this subset.

For any graph the domination number is greater than or equal to the irredundance number (A332404) and less than or equal to the independent domination number (A332402). - Andrew Howroyd, Feb 13 2020

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,     708,     152,    21,    5,   1,  1;
    1044,    9384,    1724,   166,   21,   5,  1, 1;
   12346,  221135,   38996,  1997,  166,  21,  5, 1, 1;
  274668, 9877969, 1800340, 49961, 2036, 166, 21, 5, 1, 1;
  ...
		

Links

• FindStat - Combinatorial Statistic Finder, The domination number of a graph.
• Eric Weisstein's World of Mathematics, Domination Number

Crossrefs

Row sums are A000088.

Columns k=1..2 are A000088(n-1), A332625.

Cf. A263341, A332400, A332401, A332402, A332403, A332404, A332405.

Formula

T(n,k) = T(n-1,k-1) for 2*(k-1) >= n. - Andrew Howroyd, Feb 17 2020

Extensions

Extended to 10 rows by Eric W. Weisstein, May 18 2017