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Domination number for knight graph on an n X n toroidal board.
3

%I #20 Mar 09 2024 19:20:27

%S 1,2,3,4,5,6,9,8,12,15,18,21,25,28,33,32

%N Domination number for knight graph on an n X n toroidal board.

%C That is, the minimal number of knights needed to cover an n X n toroidal chessboard so that every square either has a knight on it, or is under attack by a knight, or both.

%D John J. Watkins, Across the Board: The Mathematics of Chessboard Problem, Princeton University Press, 2004, pages 140-144.

%H Andy Huchala, <a href="/A279407/a279407_1.py.txt">Python program</a>.

%e For an 8 X 8 board, the solution is:

%e N . . . . . . N

%e . . . . . . . .

%e . . N . . N . .

%e . . . . . . . .

%e . . . N N . . .

%e . . . . . . . .

%e . N . . . . N .

%e . . . . . . . .

%Y Cf. A006075, A279402.

%K nonn,hard,more

%O 1,2

%A _Andrey Zabolotskiy_, Dec 12 2016

%E a(9)-a(16) from _Andy Huchala_, Mar 03 2024