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A075324
Independent domination number for queens' graph Q(n).
10
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
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.
Juho Lauri, Improved bounds on the domatic numbers of queens graphs, Disc. Math. Lett. 16 (2025) 94-99. See p. 2, Table 1.1.
EXAMPLE
a(8) = 5 queens attacking all squares of standard chessboard:
. . . . . . . .
. . . . . Q . .
. . Q . . . . .
. . . . Q . . .
. . . . . . Q .
. . . Q . . . .
. . . . . . . .
. . . . . . . .
CROSSREFS
A002567 gives the number of solutions.
Cf. A075458 (not necessarily independent).
Sequence in context: A130250 A130253 A145288 * A134993 A011375 A119661
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 Andrei Zabolotskii, 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