A350820 Array read by antidiagonals: T(m,n) is the number of minimum dominating sets in the grid graph P_m X P_n.

1, 2, 2, 1, 6, 1, 4, 3, 3, 4, 3, 12, 10, 12, 3, 1, 2, 29, 29, 2, 1, 8, 17, 1, 2, 1, 17, 8, 4, 2, 2, 52, 52, 2, 2, 4, 1, 20, 11, 92, 22, 92, 11, 20, 1, 13, 2, 46, 2, 13, 13, 2, 46, 2, 13, 5, 24, 1, 4, 3, 288, 3, 4, 1, 24, 5, 1, 2, 3, 324, 344, 34, 34, 344, 324, 3, 2, 1

Offset

1,2

Comments

The domination number of the grid graphs is tabulated in A350823.

Links

Stephan Mertens, Table of n, a(n) for n = 1..946 (first 276 terms from Andrew Howroyd)

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, Grid Graph

Eric Weisstein's World of Mathematics, Minimum Dominating Set

Formula

T(m,n) = T(n,m).

Example

Table begins:
===================================
m\n | 1  2  3  4   5   6  7   8
----+------------------------------
  1 | 1  2  1  4   3   1  8   4 ...
  2 | 2  6  3 12   2  17  2  20 ...
  3 | 1  3 10 29   1   2 11  46 ...
  4 | 4 12 29  2  52  92  2   4 ...
  5 | 3  2  1 52  22  13  3 344 ...
  6 | 1 17  2 92  13 288 34   2 ...
  7 | 8  2 11  2   3  34  2  34 ...
  8 | 4 20 46  4 344   2 34  52 ...
  ...

Crossrefs

Rows 1..4 are A347633, A347558, A350821, A350822.

Main diagonal is A347632.

Cf. A218354 (dominating sets), A286847 (minimal dominating sets), A303293, A350815, A350823.

Sequence in context: A326617 A371727 A326962 * A371886 A280245 A290013

Adjacent sequences: A350817 A350818 A350819 * A350821 A350822 A350823

Keyword

nonn,look,tabl

Author

Andrew Howroyd, Jan 17 2022

Status

approved