A332400 - OEIS

A332400

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

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OFFSET

2,2

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.

LINKS

Table of n, a(n) for n=2..46.

Eric Weisstein's World of Mathematics, Total Domination Number

Wikipedia, Dominating set

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.

EXAMPLE

Triangle begins, n >= 2, k >= 2:

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;

...

CROSSREFS

Column k=2 is A332406.

Row sums are A002494.

Cf. A263284, A286958.

Sequence in context: A322481 A262886 A138701 * A355143 A274878 A050821

Adjacent sequences: A332397 A332398 A332399 * A332401 A332402 A332403

KEYWORD

nonn,tabl,more

AUTHOR

Andrew Howroyd, Feb 11 2020

STATUS

approved