A332400 -id:A332400 - cp's OEIS frontend

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

Christian Stump, Oct 13 2015

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

			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;
  ...

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

Row sums are A000088.
Columns k=1..2 are A000088(n-1), A332625.
Cf. A263341, A332400, A332401, A332402, A332403, A332404, A332405.

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

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

A286958 Triangle read by rows: T(n,k) is the number of graphs with n vertices with connected domination number k.

Original entry on oeis.org

1, 1, 2, 4, 2, 11, 8, 2, 34, 62, 14, 2, 156, 514, 163, 18, 2, 1044, 7147, 2583, 317, 24, 2, 12346, 170803, 70667, 6720, 513, 29, 2, 274668, 7613603, 3566498, 247454, 13525, 785, 36, 2

Offset: 1

Eric W. Weisstein, May 17 2017

			Triangle begins:
    1;
    1;
    2;
    4,   2;
   11,   8,   2;
   34,  62,  14,  2;
  156, 514, 163, 18, 2;
  ...

Eric Weisstein's World of Mathematics, Connected Domination Number.

Row sums are A001349.
Column k=1 is A000088(n-1).
Cf. A263284, A332400, A332401.

A332406 Number of simple graphs on n unlabeled nodes with total domination number 2.

Original entry on oeis.org

0, 1, 2, 6, 19, 96, 670, 8191, 183149, 7888271

Offset: 1

Andrew Howroyd, Feb 13 2020

Eric Weisstein's World of Mathematics, Total Domination Number.

Column k=2 of A332400.

cp's OEIS Frontend

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

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A286958 Triangle read by rows: T(n,k) is the number of graphs with n vertices with connected domination number k.

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Author

Keywords

Examples

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A332406 Number of simple graphs on n unlabeled nodes with total domination number 2.

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Author

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