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Array read by antidiagonals: T(m,n) is the number of minimum dominating sets in the grid graph P_m X P_n.
8

%I #15 Dec 05 2024 20:06:27

%S 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,

%T 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,

%U 1,4,3,288,3,4,1,24,5,1,2,3,324,344,34,34,344,324,3,2,1

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

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

%H Stephan Mertens, <a href="/A350820/b350820.txt">Table of n, a(n) for n = 1..946</a> (first 276 terms from Andrew Howroyd)

%H Stephan Mertens, <a href="https://arxiv.org/abs/2408.08053">Domination Polynomials of the Grid, the Cylinder, the Torus, and the King Graph</a>, arXiv:2408.08053 [math.CO], Aug 2024.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GridGraph.html">Grid Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>

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

%e Table begins:

%e ===================================

%e m\n | 1 2 3 4 5 6 7 8

%e ----+------------------------------

%e 1 | 1 2 1 4 3 1 8 4 ...

%e 2 | 2 6 3 12 2 17 2 20 ...

%e 3 | 1 3 10 29 1 2 11 46 ...

%e 4 | 4 12 29 2 52 92 2 4 ...

%e 5 | 3 2 1 52 22 13 3 344 ...

%e 6 | 1 17 2 92 13 288 34 2 ...

%e 7 | 8 2 11 2 3 34 2 34 ...

%e 8 | 4 20 46 4 344 2 34 52 ...

%e ...

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

%Y Main diagonal is A347632.

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

%K nonn,look,tabl

%O 1,2

%A _Andrew Howroyd_, Jan 17 2022