cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-7 of 7 results.

A263341 Triangle read by rows: T(n,k) is the number of unlabeled simple graphs on n vertices with independence number k.

Original entry on oeis.org

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
Offset: 1

Views

Author

Christian Stump, Oct 15 2015

Keywords

Comments

The independence number of a graph is the maximum size of an independent set.
Row sums give A000088, n >= 1.
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

Examples

			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;
  ...
		

Crossrefs

Row sums are A000088.
Transpose of A287024.
Cf. A115196, A126744 (clique number of connected graphs), A294490 (independence number of connected graphs).

Extensions

a(21)-a(28) from Geoffrey Critzer, Sep 22 2016
Rows 8-10 from Eric W. Weisstein, May 16 2017
Rows 11-13 from Brendan McKay, Feb 18 2020
Name clarified by Andrew Howroyd, Feb 18 2020

A024607 Number of connected triangle-free graphs on n unlabeled nodes.

Original entry on oeis.org

1, 1, 1, 3, 6, 19, 59, 267, 1380, 9832, 90842, 1144061, 19425052, 445781050, 13743625184, 566756900370, 31125101479652
Offset: 1

Views

Author

Keywords

Crossrefs

Inverse Euler transform of A006785.
Table of graphs on n nodes with clique number k is A126744.
Column k=1 of A283417.

Extensions

2 more terms from Vladeta Jovovic, May 17 2008
2 more terms from A006785 by Martin Fuller, May 01 2015

A126745 Number of connected graphs on n nodes with clique number 3.

Original entry on oeis.org

0, 0, 1, 2, 11, 63, 477, 5339, 94535, 2774240, 135794730
Offset: 1

Views

Author

N. J. A. Sloane, Feb 18 2007

Keywords

Crossrefs

A diagonal of triangle in A126744.

Extensions

a(11) from Michael Sollami, Jan 29 2012

A126746 Number of connected graphs on n nodes with clique number 4.

Original entry on oeis.org

0, 0, 0, 1, 3, 25, 266, 4646, 136935, 7121703, 647596643
Offset: 1

Views

Author

N. J. A. Sloane, Feb 18 2007

Keywords

Crossrefs

A diagonal of triangle in A126744.

Extensions

a(11) from Michael Sollami, Jan 29 2012

A126747 Number of connected graphs on n nodes with clique number 5.

Original entry on oeis.org

0, 0, 0, 0, 1, 4, 45, 785, 26205, 1696407, 209046708
Offset: 1

Views

Author

N. J. A. Sloane, Feb 18 2007

Keywords

Crossrefs

A diagonal of triangle in A126744.

Extensions

a(11) from Michael Sollami, Jan 29 2012

A126748 Number of connected graphs on n nodes with clique number 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 5, 73, 1908, 110140, 13779220
Offset: 1

Views

Author

N. J. A. Sloane, Feb 18 2007

Keywords

Crossrefs

A diagonal of triangle in A126744.

Extensions

a(11) from Michael Sollami, Jan 29 2012

A217987 Number of connected graphs on n nodes with clique number 7.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 6, 109, 4085
Offset: 1

Views

Author

Arkadiusz Wesolowski, Oct 17 2012

Keywords

Crossrefs

A diagonal of triangle in A126744.

Extensions

Offset set to 1 by Travis Hoppe, Apr 22 2014
Showing 1-7 of 7 results.