A263284 Triangle read by rows: T(n,k) is the number of 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

1,4

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

Links

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

FindStat - Combinatorial Statistic Finder, The domination number of a graph.

Eric Weisstein's World of Mathematics, Domination Number

Formula

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

Example

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;
  ...

Crossrefs

Row sums are A000088.

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

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

Sequence in context: A291261 A294206 A332402 * A332404 A308905 A158471

Adjacent sequences: A263281 A263282 A263283 * A263285 A263286 A263287

Keyword

nonn,tabl,more

Author

Christian Stump, Oct 13 2015

Extensions

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

Status

approved