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A263341
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Triangle read by rows: T(n,k) is the number of unlabeled graphs on n vertices with independence number k.
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19
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1, 1, 1, 1, 2, 1, 1, 6, 3, 1, 1, 13, 15, 4, 1, 1, 37, 82, 30, 5, 1, 1, 106, 578, 301, 51, 6, 1, 1, 409, 6021, 4985, 842, 80, 7, 1, 1, 1896, 101267, 142276, 27107, 1995, 117, 8, 1, 1, 12171, 2882460, 7269487, 1724440, 112225, 4210, 164, 9, 1, 1, 105070, 138787233, 655015612, 210799447, 13893557, 388547, 8165, 221, 10, 1
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OFFSET
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1,5
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COMMENTS
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The independence number of a graph is the maximum size of an independent set.
T(n,k) is also the number of graphs on n vertices such that a largest clique is of size k. - Geoffrey Critzer, Sep 23 2016
T(n,k) is also the number of graphs on n vertices such that the size of a smallest vertex cover is n-k. - Geoffrey Critzer, Sep 23 2016
T(n,k) is also the number of graphs on n vertices with independence number k. - Eric W. Weisstein, May 17 2017
For any graph the independence number is greater than or equal to the independent domination number (A332402) and less than or equal to the upper domination number (A332403). - Andrew Howroyd, Feb 19 2020
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LINKS
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EXAMPLE
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Triangle begins:
1;
1, 1;
1, 2, 1;
1, 6, 3, 1;
1, 13, 15, 4, 1;
1, 37, 82, 30, 5, 1;
1, 106, 578, 301, 51, 6, 1;
1, 409, 6021, 4985, 842, 80, 7, 1;
1, 1896, 101267, 142276, 27107, 1995, 117, 8, 1;
1, 12171, 2882460, 7269487, 1724440, 112225, 4210, 164, 9, 1;
...
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CROSSREFS
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Cf. A115196, A126744 (clique number of connected graphs), A294490 (independence number of connected graphs).
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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