A332400 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with total domination number k, n >= 2, 2 <= k <= n.

1, 2, 0, 6, 0, 1, 19, 2, 2, 0, 96, 14, 11, 0, 1, 670, 163, 51, 2, 2, 0, 8191, 2583, 495, 21, 11, 0, 1, 183149, 70667, 8127, 314, 61, 2, 2, 0, 7888271, 3566498, 268125, 6929, 644, 21, 11, 0, 1

Offset: 2

Author

Andrew Howroyd, Feb 11 2020

Keywords

• nonn
• tabl
• more

Comments

Only graphs without isolated nodes can have a total dominating set.

The total domination number of a graph is greater than or equal to the domination number.

Examples

			Triangle begins, n >= 2, k >= 2:
        1;
        2,       0;
        6,       0,      1;
       19,       2,      2,    0;
       96,      14,     11,    0,   1;
      670,     163,     51,    2,   2,  0;
     8191,    2583,    495,   21,  11,  0,  1;
   183149,   70667,   8127,  314,  61,  2,  2, 0;
  7888271, 3566498, 268125, 6929, 644, 21, 11, 0, 1;
  ...
		

Links

• Eric Weisstein's World of Mathematics, Total Domination Number
• Wikipedia, Dominating set

Crossrefs

Column k=2 is A332406.

Row sums are A002494.

Cf. A263284, A286958.

Formula

T(2*n, 2*n) = 1; T(2*n+1, 2*n) = 2; T(2*n+1, 2*n+1) = T(2*n+2, 2*n+1) = 0.