A382206 Number of minimum connected dominating sets in the n X n king graph.

1, 4, 1, 21, 1, 21, 843, 720, 556841, 99357, 458, 32, 3600, 30580044, 826720, 4

Offset: 1

Author

Eric W. Weisstein, Mar 18 2025

Keywords

• nonn
• more

Comments

a(1)-a(8) computed with ILP based on a Mathematica implementation by Stan Wagon using an idea from Rob Pratt.

Links

• Eric Weisstein's World of Mathematics, Connected Dominating Set.
• Eric Weisstein's World of Mathematics, King Graph.
• Eric W. Weisstein, Symmetrically inequivalent minimum configurations with multiplicities for n = 1 to 6
• Eric W. Weisstein, Symmetrically inequivalent minimum configurations with multiplicities for n = 7
• Eric W. Weisstein, Symmetrically inequivalent minimum configurations with multiplicities for n = 8
• Eric W. Weisstein, Symmetrically inequivalent minimum configurations with multiplicities for n = 16

Crossrefs

Cf. A289180, A347554, A381730.

Cf. A370428 (connected domination numbers).

Extensions

a(8)-a(16) from Andrew Howroyd, Mar 19 2025