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A075324 Independent domination number for queens' graph Q(n). 6

%I #50 Feb 03 2023 20:42:16

%S 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,

%T 16,16,17

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

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

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

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

%H William Herbert Bird, <a href="https://dspace.library.uvic.ca/handle/1828/8634">Computational methods for domination problems</a>, University of Victoria, 2017. See Table 5.1 on p. 114.

%H Matthew D. Kearse and Peter B. Gibbons, <a href="http://ajc.maths.uq.edu.au/pdf/23/ocr-ajc-v23-p253.pdf">Computational Methods and New Results for Chessboard Problems</a>, Australasian Journal of Combinatorics 23 (2001), 253-284.

%H Alexis Langlois-Rémillard, Christoph Müßig, and Érika Róldan, <a href="https://arxiv.org/abs/2211.05651">Complexity of Chess Domination Problems</a>, arXiv:2211.05651 [math.CO], 2022.

%H Alexis Langlois-Rémillard, Christoph Müßig, and Érika Róldan, <a href="https://gist.github.com/PhoenixSmaug/16685620ebd46472ddbd1c961f69672a">Solution a(26)-a(31) and Julia code to compute the sequence</a>, 2022.

%e a(8) = 5 queens attacking all squares of standard chessboard:

%e . . . . . . . .

%e . . . . . Q . .

%e . . Q . . . . .

%e . . . . Q . . .

%e . . . . . . Q .

%e . . . Q . . . .

%e . . . . . . . .

%e . . . . . . . .

%Y A002567 gives the number of solutions.

%K nonn,more

%O 1,4

%A _N. J. A. Sloane_, Oct 16 2002

%E a(19)-a(24) from Bird and a(25) from Kearse & Gibbons added by _Andrey Zabolotskiy_, Sep 03 2021

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

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

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Last modified April 18 18:49 EDT 2024. Contains 371781 sequences. (Running on oeis4.)