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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
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
Sequence in context: A136597 A064329 A187740 * A358297 A209035 A230782
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.)