A347554 Number of minimum dominating sets in the n X n king graph.

1, 4, 1, 256, 79, 1, 243856, 3600, 1, 581571283, 281585, 1, 2722291223553, 32581328, 1, 21706368614058886, 5112264019, 1, 268740319616196074546, 1028516654620, 1, 4839916638142874877046813

Offset: 1

Author

Eric W. Weisstein, Sep 06 2021

Keywords

• nonn
• more

Comments

a(3*n) = 1 for all n, since the 3n X 3n king graph has domination number n^2 and the only way to achieve this is if each of the n^2 kings is placed in the middle of its own 3 X 3 square.

Links

• Stephan Mertens, Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph, arXiv:2408.08053 [math.CO], Aug 2024.
• Eric Weisstein's World of Mathematics, King Graph
• Eric Weisstein's World of Mathematics, Minimum Dominating Set
• Eric W. Weisstein, Unique minimum dominating set on a 3n X 3n king graph

Crossrefs

Main diagonal of A350815.

Cf. A075561 (domination number of the n X n king graph), A133791, A286881.

Extensions

a(7)-a(12) from Andrew Howroyd, Jan 17 2022

a(13)-a(22) from Stephan Mertens, Aug 18 2024