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A332400 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with total domination number k, n >= 2, 2 <= k <= n.

%I A332400 #12 Feb 16 2025 08:33:59
%S A332400 1,2,0,6,0,1,19,2,2,0,96,14,11,0,1,670,163,51,2,2,0,8191,2583,495,21,
%T A332400 11,0,1,183149,70667,8127,314,61,2,2,0,7888271,3566498,268125,6929,
%U A332400 644,21,11,0,1
%N A332400 Triangle read by rows: T(n,k) is the number of simple graphs on n unlabeled nodes with total domination number k, n >= 2, 2 <= k <= n.
%C A332400 Only graphs without isolated nodes can have a total dominating set.
%C A332400 The total domination number of a graph is greater than or equal to the domination number.
%H A332400 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TotalDominationNumber.html">Total Domination Number</a>
%H A332400 Wikipedia, <a href="https://en.wikipedia.org/wiki/Dominating_set">Dominating set</a>
%F A332400 T(2*n, 2*n) = 1; T(2*n+1, 2*n) = 2;  T(2*n+1, 2*n+1) = T(2*n+2, 2*n+1) = 0.
%e A332400 Triangle begins, n >= 2, k >= 2:
%e A332400         1;
%e A332400         2,       0;
%e A332400         6,       0,      1;
%e A332400        19,       2,      2,    0;
%e A332400        96,      14,     11,    0,   1;
%e A332400       670,     163,     51,    2,   2,  0;
%e A332400      8191,    2583,    495,   21,  11,  0,  1;
%e A332400    183149,   70667,   8127,  314,  61,  2,  2, 0;
%e A332400   7888271, 3566498, 268125, 6929, 644, 21, 11, 0, 1;
%e A332400   ...
%Y A332400 Column k=2 is A332406.
%Y A332400 Row sums are A002494.
%Y A332400 Cf. A263284, A286958.
%K A332400 nonn,tabl,more
%O A332400 2,2
%A A332400 _Andrew Howroyd_, Feb 11 2020