A075324 Independent domination number for queens' graph Q(n).

1, 1, 1, 3, 3, 4, 4, 5, 5, 5, 5, 7, 7, 8, 9, 9, 9, 10, 11, 11, 11, 12, 13, 13, 13, 14, 15, 15, 16, 16, 17

Offset

1,4

References

W. W. R. Ball and H. S. M. Coxeter, Math'l Rec. and Essays, 13th Ed. Dover, p. 173.

C. Berge, Graphs and Hypergraphs, North-Holland, 1973; p. 304, Example 2.

M. A. Sainte-Laguë, Les Réseaux (ou Graphes), Mémorial des Sciences Mathématiques, Fasc. 18, Gauthier-Villars, Paris, 1926, p. 49.

Links

Table of n, a(n) for n=1..31.

William Herbert Bird, Computational methods for domination problems, University of Victoria, 2017. See Table 5.1 on p. 114.

Matthew D. Kearse and Peter B. Gibbons, Computational Methods and New Results for Chessboard Problems, Australasian Journal of Combinatorics 23 (2001), 253-284.

Alexis Langlois-Rémillard, Christoph Müßig, and Érika Róldan, Complexity of Chess Domination Problems, arXiv:2211.05651 [math.CO], 2022.

Alexis Langlois-Rémillard, Christoph Müßig, and Érika Róldan, Solution a(26)-a(31) and Julia code to compute the sequence, 2022.

Example

a(8) = 5 queens attacking all squares of standard chessboard:
  . . . . . . . .
  . . . . . Q . .
  . . Q . . . . .
  . . . . Q . . .
  . . . . . . Q .
  . . . Q . . . .
  . . . . . . . .
  . . . . . . . .

Crossrefs

A002567 gives the number of solutions.

Sequence in context: A130250 A130253 A145288 * A134993 A011375 A119661

Adjacent sequences: A075321 A075322 A075323 * A075325 A075326 A075327

Keyword

nonn,more

Author

N. J. A. Sloane, Oct 16 2002

Extensions

a(19)-a(24) from Bird and a(25) from Kearse & Gibbons added by Andrey Zabolotskiy, Sep 03 2021

a(26) from Alexis Langlois-Rémillard, Christoph Müßig and Érika Roldán added by Christoph Muessig, Aug 25 2022

a(27)-a(31) from Alexis Langlois-Rémillard, Christoph Müßig and Érika Roldán added by Christoph Muessig, Sep 19 2022

Status

approved