A103315 Number of minimum dominating sets for the n X n knight graph.

1, 1, 8, 9, 47, 127, 10, 2, 2, 4, 800, 2, 152, 4, 504, 2, 212, 19562

Offset: 1

Author

N. J. A. Sloane, Mar 20 2005, following a suggestion from Lee Morgenstern

Keywords

• nonn
• more

Comments

In other words, as made explicit in the old name: Sequence A006075 gives minimum number of knights needed to cover an n X n board (i.e., the domination number of the n X n knight graph). This sequence (A103315) gives total number of solutions using A006075(n) knights (compare A006076).

Links

• Lee Morgenstern, Knight Domination.
• Frank Rubin, Knight coverings for large chessboards, 2000.
• Eric Weisstein's World of Mathematics, Knight Graph
• Eric Weisstein's World of Mathematics, Minimum Dominating Set

Crossrefs

Cf. A006075 (domination number of the n X n knight graph).

Cf. A006076 (inequivalent number of minimum dominating sets).

Cf. A098604.

Extensions

New name from Eric W. Weisstein, Sep 06 2021