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Array read by antidiagonals: T(m,n) = number of minimum dominating sets in the stacked prism graph C_m X P_n.
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%I #34 Aug 20 2024 13:19:25

%S 1,2,2,1,6,3,4,3,9,6,3,12,34,4,5,1,2,123,4,10,3,8,17,3,16,5,51,14,4,2,

%T 18,28,290,18,14,8,1,20,93,76,320,6,63,4,3,13,2,438,164,265,171,14,4,

%U 18,25,5,24,3,396,255,36,91,24,9,120,11,1,2,27,904,250,6,1526,60,2052,25,22,3

%N Array read by antidiagonals: T(m,n) = number of minimum dominating sets in the stacked prism graph C_m X P_n.

%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="https://mathworld.wolfram.com/MinimumDominatingSet.html">Minimum Dominating Set</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StackedPrismGraph.html">Stacked Prism Graph</a>.

%e Table starts:

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

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

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

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

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

%e 3 | 3 9 34 123 3 18 ...

%e 4 | 6 4 4 16 28 76 ...

%e 5 | 5 10 5 290 320 265 ...

%e ...

%Y Main diagonal is A375569.

%Y Rows 1..2 are A347633, A347558.

%Y Column 1 is A347538, column 2 is essentially A347634.

%Y Cf. A286514, A350820, A375603.

%K nonn,tabl,hard

%O 1,2

%A _Stephan Mertens_, Aug 19 2024