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 A332407 Number of simple graphs on n unlabeled nodes with upper domination number greater than independence number. 1
 0, 0, 0, 0, 0, 1, 6, 85, 2574, 193486 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,7 COMMENTS The upper domination number of a graph is the maximum cardinality of a minimal dominating set. For any graph the upper domination number is greater than or equal to the independence number. This sequence gives the number of graphs where it is strictly greater than. The m X n rook graphs with 2 <= m < n are a class of graph with this property because the independence number is m, and a row of n rooks is minimally dominating. LINKS Table of n, a(n) for n=1..10. Eric Weisstein's World of Mathematics, Independence Number Eric Weisstein's World of Mathematics, Minimal Dominating Set Eric Weisstein's World of Mathematics, Rook Graph EXAMPLE The a(6) = 1 graph illustrated below has independence number 2 and upper domination number 3. *--------o | \ / | | *--o | | / \ | *--------o The above graph is the 2 X 3 rook graph, drawn to show all edges. The three vertices marked with an asterisk are a minimal dominating set. CROSSREFS Cf. A263341, A332403. Sequence in context: A136597 A064329 A187740 * A358297 A209035 A230782 Adjacent sequences: A332404 A332405 A332406 * A332408 A332409 A332410 KEYWORD nonn,more AUTHOR Andrew Howroyd, Feb 15 2020 STATUS approved

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Last modified April 18 16:22 EDT 2024. Contains 371780 sequences. (Running on oeis4.)