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A263284 Triangle read by rows: T(n,k) is the number of unlabeled simple graphs on n vertices with domination number k.

%I A263284 #32 Feb 16 2025 08:33:27
%S A263284 1,1,1,2,1,1,4,5,1,1,11,16,5,1,1,34,94,21,5,1,1,156,708,152,21,5,1,1,
%T A263284 1044,9384,1724,166,21,5,1,1,12346,221135,38996,1997,166,21,5,1,1,
%U A263284 274668,9877969,1800340,49961,2036,166,21,5,1,1
%N A263284 Triangle read by rows: T(n,k) is the number of unlabeled simple graphs on n vertices with domination number k.
%C A263284 The domination number of a graph is given by the minimum size of a dominating set of vertices. A dominating set of vertices is a subset of the vertex set of such that every vertex is either in this subset or adjacent to an element of this subset.
%C A263284 For any graph the domination number is greater than or equal to the irredundance number (A332404) and less than or equal to the independent domination number (A332402). - _Andrew Howroyd_, Feb 13 2020
%H A263284 FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000273">The domination number of a graph.</a>
%H A263284 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/DominationNumber.html">Domination Number</a>
%F A263284 T(n,k) = T(n-1,k-1) for 2*(k-1) >= n. - _Andrew Howroyd_, Feb 17 2020
%e A263284 Triangle begins:
%e A263284        1;
%e A263284        1,       1;
%e A263284        2,       1,       1;
%e A263284        4,       5,       1,     1;
%e A263284       11,      16,       5,     1,    1;
%e A263284       34,      94,      21,     5,    1,   1;
%e A263284      156,     708,     152,    21,    5,   1,  1;
%e A263284     1044,    9384,    1724,   166,   21,   5,  1, 1;
%e A263284    12346,  221135,   38996,  1997,  166,  21,  5, 1, 1;
%e A263284   274668, 9877969, 1800340, 49961, 2036, 166, 21, 5, 1, 1;
%e A263284   ...
%Y A263284 Row sums are A000088.
%Y A263284 Columns k=1..2 are A000088(n-1), A332625.
%Y A263284 Cf. A263341, A332400, A332401, A332402, A332403, A332404, A332405.
%K A263284 nonn,tabl,more
%O A263284 1,4
%A A263284 _Christian Stump_, Oct 13 2015
%E A263284 Extended to 10 rows by _Eric W. Weisstein_, May 18 2017