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 A263284 Triangle read by rows: T(n,k) is the number of graphs on n vertices with domination number k. 9
 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, 1044, 9384, 1724, 166, 21, 5, 1, 1, 12346, 221135, 38996, 1997, 166, 21, 5, 1, 1, 274668, 9877969, 1800340, 49961, 2036, 166, 21, 5, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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. 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 LINKS Table of n, a(n) for n=1..55. FindStat - Combinatorial Statistic Finder, The domination number of a graph. Eric Weisstein's World of Mathematics, Domination Number FORMULA T(n,k) = T(n-1,k-1) for 2*(k-1) >= n. - Andrew Howroyd, Feb 17 2020 EXAMPLE Triangle begins: 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; 1044, 9384, 1724, 166, 21, 5, 1, 1; 12346, 221135, 38996, 1997, 166, 21, 5, 1, 1; 274668, 9877969, 1800340, 49961, 2036, 166, 21, 5, 1, 1; ... CROSSREFS Row sums are A000088. Columns k=1..2 are A000088(n-1), A332625. Cf. A263341, A332400, A332401, A332402, A332403, A332404, A332405. Sequence in context: A291261 A294206 A332402 * A332404 A308905 A158471 Adjacent sequences: A263281 A263282 A263283 * A263285 A263286 A263287 KEYWORD nonn,tabl,more AUTHOR Christian Stump, Oct 13 2015 EXTENSIONS Extended to 10 rows by Eric W. Weisstein, May 18 2017 STATUS approved

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Last modified April 12 20:38 EDT 2024. Contains 371639 sequences. (Running on oeis4.)