A084268 -id:A084268 - cp's OEIS frontend

A076278 Number of 2-chromatic (i.e., chromatic number equals 2) simple graphs on n nodes.

0, 1, 2, 6, 12, 34, 87, 302, 1118, 5478, 32302, 251134, 2527711, 33985852, 611846939, 14864650923, 488222721991, 21712049275197, 1308300679611468, 106897965189674290, 11852113048215107821, 1784730721403509209214, 365323537513403184463272

Offset: 1

Eric W. Weisstein, Oct 06 2002

nonn

Andrew Howroyd, Table of n, a(n) for n = 1..50
Keith M. Briggs, Combinatorial Graph Theory
Eric Weisstein's World of Mathematics, n-Chromatic Graph

Column k=2 of A084268.

Cf. A076279, A076280, A076281, A076282, A115597.

A005142 = Import["https://oeis.org/A005142/b005142.txt", "Table"][[All, 2]];
etr[p_] := Module[{b}, b[n_] := b[n] = If[n == 0, 1, Sum[Sum[d*p[d], {d, Divisors[j]}]*b[n - j], {j, 1, n}]/n]; b];
a = etr[A005142[[# + 1]]&][#] - 1&;
Array[a, 23] (* Jean-François Alcover, Sep 03 2019 *)

a(n) = A033995(n)-1.

More terms from Vladeta Jovovic, Jul 31 2003

Terms a(21) and beyond from Andrew Howroyd, Sep 05 2018

A076279 Number of 3-chromatic (i.e., chromatic number equals 3) simple graphs on n nodes.

Original entry on oeis.org

0, 0, 1, 3, 16, 84, 579, 5721, 87381, 2104349, 78315231, 4383566676, 362178638727

Offset: 1

Eric W. Weisstein, Oct 06 2002

Keith M. Briggs, Combinatorial Graph Theory
Eric Weisstein's World of Mathematics, n-Chromatic Graph

Column k=3 of A084268.

Cf. A076278, A076280, A076281, A076282, A115597.

a(10) from Keith Briggs, Mar 14 2006
a(11) from Michael Sollami, Jan 28 2012
a(12)-a(13) from Brendan McKay, Nov 08 2022

A076281 Number of 5-chromatic (i.e., chromatic number equals 5) simple graphs on n nodes.

Original entry on oeis.org

0, 0, 0, 0, 1, 5, 52, 867, 28722, 1919895, 250530482

Offset: 1

Eric W. Weisstein, Oct 06 2002

Keith M. Briggs, Combinatorial Graph Theory
Eric Weisstein's World of Mathematics, n-Chromatic Graph

Column k=5 of A084268.

Cf. A076278, A076279, A076280, A076282.

a(10) from Keith Briggs, Mar 14 2006

a(11) from Michael Sollami, Jan 28 2012

A076280 Number of 4-chromatic (i.e., chromatic number equals 4) simple graphs on n nodes.

Original entry on oeis.org

0, 0, 0, 1, 4, 31, 318, 5366, 155291, 7855628, 675054876

Offset: 1

Eric W. Weisstein, Oct 06 2002

Keith M. Briggs, Combinatorial Graph Theory
Eric Weisstein's World of Mathematics, n-Chromatic Graph

Column k=4 of A084268.

Cf. A076278, A076279, A076281, A076282.

a(10) from Keith Briggs, Feb 24 2006

a(11) from Michael Sollami, Jan 28 2012

A076282 Number of 6-chromatic (i.e., chromatic number equals 6) simple graphs on n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 6, 81, 2028, 115391, 14662562

Offset: 1

Eric W. Weisstein, Oct 06 2002

Keith M. Briggs, Combinatorial Graph Theory
Eric Weisstein's World of Mathematics, n-Chromatic Graph

Column k=6 of A084268.

Cf. A076278, A076279, A076280, A076281.

a(10) from Keith Briggs, Mar 14 2006

a(11) from Michael Sollami, Jan 28 2012

A084269 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes having chromatic number k, 1 <= k <= n.

Original entry on oeis.org

1, 0, 1, 0, 1, 1, 0, 3, 2, 1, 0, 5, 12, 3, 1, 0, 17, 64, 26, 4, 1, 0, 44, 475, 282, 46, 5, 1, 0, 182, 5036, 5009, 809, 74, 6, 1, 0, 730, 80947, 149551, 27794, 1940, 110, 7, 1, 0, 4032, 2010328, 7694428, 1890221, 113272, 4125, 156, 8, 1, 0, 25598, 76115143, 667036310, 248580644, 14545025, 389583, 8040, 212, 9, 1

Offset: 0

Eric W. Weisstein, May 24 2003

			Triangle begins:
  1;
  0,   1;
  0,   1,     1;
  0,   3,     2,      1;
  0,   5,    12,      3,     1;
  0,  17,    64,     26,     4,    1;
  0,  44,   475,    282,    46,    5,   1;
  0, 182,  5036,   5009,   809,   74,   6, 1;
  0, 730, 80947, 149551, 27794, 1940, 110, 7, 1;
  ...

Eric Weisstein's World of Mathematics, n-Chromatic Graph

Row sums are A001349.
Columns k=3..7 are A126737, A126738, A126739, A126740, A241702.
Partial row sums include A005142, A076322, A076323, A076324, A076325, A076326, A076327, A076328.
Essentially the same table as A126736.
Cf. A084268 (not necessarily connected), A115597.

a(37)-a(66) from Andrew Howroyd, Dec 02 2018

A115597 Triangle read by rows: let a(n,k) = number of graphs on n nodes with chromatic number k; T(n,k) = a(n,n-k), n >= 2, k=0..n-2.

Original entry on oeis.org

1, 1, 2, 1, 3, 6, 1, 4, 16, 12, 1, 5, 31, 84, 34, 1, 6, 52, 318, 579, 87, 1, 7, 81, 867, 5366, 5721, 302, 1, 8, 118, 2028, 28722, 155291, 87381, 1118, 1, 9, 165, 4251, 115391, 1919895, 7855628, 2104349, 5478

Offset: 2

N. J. A. Sloane, based on email from Keith Briggs, Mar 14 2006

			Table of values of a(n,k): number of graphs on n nodes with chromatic number k
n. = .1...2...3...4....5....6.....7......8........9.......10
k.----------------------------------------------------------
2....0...1...2...6...12...34....87....302.....1118.....5478... = A076278
3....0...0...1...3...16...84...579...5721....87381..2104349... = A076279
4....0...0...0...1....4...31...318...5366...155291..7855628... = A076280
5....0...0...0...0....1....5....52....867....28722..1919895... = A076281
6....0...0...0...0....0....1.....6.....81.....2028...115391... = A076282
7....0...0...0...0....0....0.....1......7......118.....4251
8....0...0...0...0....0....0.....0......1........8......165
9....0...0...0...0....0....0.....0......0........1........9
10...0...0...0...0....0....0.....0......0........0........1
Triangle begins:
1
1 2
1 3 6
1 4 16 12
1 5 31 84 34
1 6 52 318 579 87
1 7 81 867 5366 5721 302
1 8 118 2028 28722 155291 87381 1118
1 9 165 4251 115391 1919895 7855628 2104349 5478

Keith M. Briggs, Combinatorial Graph Theory

Cf. A076278, A076279, A076280, A076281, A076282.

Cf. A084268 (essentially the same sequence).

A076283 Number of 7-chromatic (i.e., chromatic number equals 7) simple graphs on n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 7, 118, 4251, 393963

Offset: 1

Eric W. Weisstein, Oct 06 2002

Eric Weisstein's World of Mathematics, n-Chromatic Graph

Column k=7 of A084268.

Cf. A076278, A076279, A076280, A076281, A076282.

a(10)-a(11) from Michael Sollami, Jan 28 2012

A205567 Number of 8-chromatic (i.e., chromatic number equals 8) simple graphs on n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 1, 8, 165, 8214

Offset: 1

Michael Sollami, Jan 28 2012

Keith M. Briggs, Combinatorial Graph Theory
Eric Weisstein's World of Mathematics, n-Chromatic Graph

Column k=8 of A084268.

Cf. A076278, A076279, A076280, A076281.

A205568 Number of 9-chromatic (i.e., chromatic number equals 9) simple graphs on n nodes.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 0, 0, 1, 9, 222

Offset: 1

Michael Sollami, Jan 28 2012

Keith M. Briggs, Combinatorial Graph Theory
Eric Weisstein's World of Mathematics, n-Chromatic Graph

Column k=9 of A084268.

Cf. A076278, A076279, A076281, A076282.

cp's OEIS Frontend

A076278 Number of 2-chromatic (i.e., chromatic number equals 2) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

Extensions

A076279 Number of 3-chromatic (i.e., chromatic number equals 3) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Extensions

A076281 Number of 5-chromatic (i.e., chromatic number equals 5) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Extensions

A076280 Number of 4-chromatic (i.e., chromatic number equals 4) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Extensions

A076282 Number of 6-chromatic (i.e., chromatic number equals 6) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Extensions

A084269 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes having chromatic number k, 1 <= k <= n.

Views

Author

Keywords

Examples

Links

Crossrefs

Extensions

A115597 Triangle read by rows: let a(n,k) = number of graphs on n nodes with chromatic number k; T(n,k) = a(n,n-k), n >= 2, k=0..n-2.

Views

Author

Keywords

Examples

Links

Crossrefs

A076283 Number of 7-chromatic (i.e., chromatic number equals 7) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

Extensions

A205567 Number of 8-chromatic (i.e., chromatic number equals 8) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs

A205568 Number of 9-chromatic (i.e., chromatic number equals 9) simple graphs on n nodes.

Views

Author

Keywords

Links

Crossrefs