A279404 Independent domination number for queens' graph on an n X n toroidal board.

1, 1, 1, 2, 5, 4, 5, 4, 5, 5, 5, 6, 7, 7, 5, 8, 9, 10

Offset: 1

Author

Andrey Zabolotskiy, Dec 11 2016

Keywords

• nonn
• hard
• more

Comments

That is, the minimal number of queens needed to cover an n X n toroidal chessboard so that every square either has a queen on it or is under attack by a queen, but not both.

A279402(n) <= a(n) <= A085801(n).

Links

• Andy Huchala, Python program.
• Christina M. Mynhardt, Upper bounds for the domination numbers of toroidal queens graphs, Discussiones Mathematicae Graph Theory, 23 (2003), 163-175.

Crossrefs

Cf. A075324, A085801, A279402.

Formula

a(3*n) = n if n = 1, 5, 7, 11 (mod 12).

Extensions

a(17)-a(18) from Andy Huchala, Mar 09 2024