A243781 -id:A243781 - cp's OEIS frontend

A294490 Triangle read by rows: T(n,k) is the number of simple connected graphs on n vertices having independence number k.

1, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 11, 8, 1, 0, 1, 34, 63, 13, 1, 0, 1, 103, 524, 205, 19, 1, 0, 1, 405, 5863, 4308, 513, 26, 1, 0, 1, 1892, 100702, 135563, 21782, 1105, 34, 1, 0, 1, 12166, 2880002, 7161399, 1576634, 84185, 2140, 43, 1, 0, 1, 105065, 138772607, 652024627, 203380116, 12140094, 274156, 3845, 53, 1, 0

Offset: 1

Andrew Howroyd, Oct 31 2017

Bivariate inverse Euler transform of A263341. This sequence can be derived from A263341 because the independence number of a disconnected graph is the sum of the independence numbers of its components. - Andrew Howroyd, Feb 19 2020

			Triangle begins:
  1;
  1,   0;
  1,   1,    0;
  1,   4,    1,    0;
  1,  11,    8,    1,   0;
  1,  34,   63,   13,   1,  0;
  1, 103,  524,  205,  19,  1, 0;
  1, 405, 5863, 4308, 513, 26, 1, 0;
  ...

Andrew Howroyd, Table of n, a(n) for n = 1..91 (first 13 rows derived from Brendan McKay data in A263341)

Columns 2..5 are A243781, A243782, A243783, A243784.
Row sums give A001349.
Cf. A263341 (not necessarily connected).

Terms a(56) and beyond derived from A263341 added by Andrew Howroyd, Feb 19 2020

A243782 Number of simple connected graphs on n nodes whose independence number a(g)=3.

Original entry on oeis.org

0, 0, 0, 1, 8, 63, 524, 5863, 100702, 2880002

Offset: 1

Travis Hoppe and Anna Petrone, Jun 20 2014

The independence number of a graph is the cardinality of the largest independent vertex set.

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
Travis Hoppe and Anna Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
Eric Weisstein's World of Mathematics, Independence Number, Maximum Independent Vertex Set

Column 3 of A294490.

Cf. Values of a(g) for simple connected graphs, A243781, A243782, A243783, A243784.

A243783 Number of simple connected graphs on n nodes whose independence number a(g)=4.

Original entry on oeis.org

0, 0, 0, 0, 1, 13, 205, 4308, 135563, 7161399

Offset: 1

Travis Hoppe and Anna Petrone, Jun 20 2014

The independence number of a graph is the cardinality of the largest independent vertex set.

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
Travis Hoppe and Anna Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
Eric Weisstein's World of Mathematics, Independence Number, Maximum Independent Vertex Set

Column 4 of A294490.

Cf. Values of a(g) for simple connected graphs, A243781, A243782, A243783, A243784.

A243784 Number of simple connected graphs on n nodes whose independence number a(g)=5.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 19, 513, 21782, 1576634

Offset: 1

Travis Hoppe and Anna Petrone, Jun 20 2014

The independence number of a graph is the cardinality of the largest independent vertex set.

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
Travis Hoppe and Anna Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
Eric Weisstein's World of Mathematics, Independence Number, Maximum Independent Vertex Set

Column 5 of A294490.

Cf. Values of a(g) for simple connected graphs, A243781, A243782, A243783, A243784.

cp's OEIS Frontend

A294490 Triangle read by rows: T(n,k) is the number of simple connected graphs on n vertices having independence number k.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Extensions

A243782 Number of simple connected graphs on n nodes whose independence number a(g)=3.

Views

Author

Keywords

Comments

Links

Crossrefs

A243783 Number of simple connected graphs on n nodes whose independence number a(g)=4.

Views

Author

Keywords

Comments

Links

Crossrefs

A243784 Number of simple connected graphs on n nodes whose independence number a(g)=5.

Views

Author

Keywords

Comments

Links

Crossrefs