A370428 Connected domination number of the n X n king graph.

1, 1, 1, 4, 5, 8, 12, 15, 20, 24, 28, 33, 39, 46, 52, 58

Offset

1,4

Comments

In other words, a(n) is the minimum number of kings that can be placed on an n X n chessboard such that (i) the occupied squares form a single connected component, and (ii) every square is either occupied by a king or adjacent to one that is.

a(17) <= 67; a(18) <= 75; a(19) <= 83; a(20) <= 92.

Links

Table of n, a(n) for n=1..16.

Alexander D. Healy, Examples of (near-)optimal connected dominating sets for n <= 20.

Eric Weisstein's World of Mathematics, Connected Domination Number.

Eric Weisstein's World of Mathematics, King Graph.

Crossrefs

Cf. A075561, A289180, A302401, A369692.

Sequence in context: A188095 A190675 A188077 * A027975 A011980 A260163

Adjacent sequences: A370425 A370426 A370427 * A370429 A370430 A370431

Keyword

nonn,more

Author

Alexander D. Healy, Feb 24 2024

Extensions

a(13)-a(16) from Andrew Howroyd, Feb 25 2024

Status

approved