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

Offset

1,2

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

Table of n, a(n) for n=1..12.

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.

Sequence in context: A262404 A299522 A300140 * A298939 A240098 A094337

Adjacent sequences: A347551 A347552 A347553 * A347555 A347556 A347557

Keyword

nonn,more

Author

Eric W. Weisstein, Sep 06 2021

Extensions

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

Status

approved