A360866 -id:A360866 - cp's OEIS frontend

A046752 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges on k nodes and degree >= 3 at each node, n >= 3, 2 <= k <= floor(2*n/3).

1, 1, 1, 1, 1, 2, 2, 1, 3, 5, 1, 4, 13, 4, 1, 6, 26, 24, 5, 1, 7, 47, 84, 38, 1, 9, 78, 233, 216, 23, 1, 11, 126, 557, 914, 314, 16, 1, 13, 188, 1193, 3077, 2270, 325, 1, 15, 276, 2355, 8915, 11592, 4015, 162, 1, 18, 391, 4370, 23008, 47079, 31443, 4495, 66

Offset: 3

N. J. A. Sloane

Original name: Triangle of number of homeomorphically irreducible stars with n edges and m nodes.

			Triangle begins:
  1;
  1;
  1,  1;
  1,  2,   2;
  1,  3,   5;
  1,  4,  13,    4;
  1,  6,  26,   24,    5;
  1,  7,  47,   84,   38;
  1,  9,  78,  233,  216,    23;
  1, 11, 126,  557,  914,   314,   16;
  1, 13, 188, 1193, 3077,  2270,  325;
  1, 15, 276, 2355, 8915, 11592, 4015, 162;
  ...

Andrew Howroyd, Table of n, a(n) for n = 3..93 (rows 3..18)
B. R. Heap, The enumeration of homeomorphically irreducible star graphs, J. Math. Phys., 7 (1966), 1582-1587.
Sean A. Irvine, Java program (github).

Row sums are A002935.
Diagonal sums are A360879.
Cf. A339160, A360866, A360870.

More terms from Sean A. Irvine, May 16 2020

Name edited and offset corrected by Andrew Howroyd, Feb 25 2023

A360867 Number of unlabeled connected loopless multigraphs with n edges and degree >= 3 at each node.

Original entry on oeis.org

0, 0, 1, 1, 2, 6, 12, 32, 92, 273, 869, 2989, 10722, 40599

Offset: 1

Andrew Howroyd, Feb 24 2023

Row sums of A360866.

Cf. A076864, A360863 (loops allowed), A360868, A360869 (not necessarily connected).

Inverse Euler transform of A360869.

A360862 Triangle read by rows: T(n,k) is the number of unlabeled connected multigraphs with n edges on k nodes and degree >= 3 at each node, loops allowed, n >= 2, 1 <= k <= floor(2*n/3).

Original entry on oeis.org

1, 1, 2, 1, 4, 1, 7, 5, 1, 10, 20, 5, 1, 14, 48, 36, 1, 18, 99, 153, 30, 1, 23, 181, 481, 277, 17, 1, 28, 303, 1239, 1451, 323, 1, 34, 479, 2811, 5572, 2946, 193, 1, 40, 726, 5805, 17607, 17343, 3806, 71, 1, 47, 1055, 11148, 48401, 77708, 36872, 3188, 1, 54, 1492, 20219, 120018, 288476, 243007, 54386, 1496

Offset: 2

Andrew Howroyd, Feb 24 2023

Terms may be computed using the tools geng, vcolg and multig in nauty with some additional processing to check the degrees of nodes.

			Triangle begins:
  1;
  1,  2;
  1,  4;
  1,  7,    5;
  1, 10,   20,     5;
  1, 14,   48,    36;
  1, 18,   99,   153,     30;
  1, 23,  181,   481,    277,     17;
  1, 28,  303,  1239,   1451,    323;
  1, 34,  479,  2811,   5572,   2946,    193;
  1, 40,  726,  5805,  17607,  17343,   3806,    71;
  1, 47, 1055, 11148,  48401,  77708,  36872,  3188;
  1, 54, 1492, 20219, 120018, 288476, 243007, 54386, 1496;
  ...

Brendan McKay and Adolfo Piperno, nauty and Traces

Column 2 is A014616.
Row sums are A360863.
Diagonal sums are A360864.
Cf. A322115, A327615, A360866 (loopless).

A360870 Triangle read by rows: T(n,k) is the number of unlabeled connected multigraphs with n edges on k nodes, no cut-points and degree >= 3 at each node, loops allowed, n >= 2, 1 <= k <= floor(2*n/3).

Original entry on oeis.org

1, 1, 2, 1, 4, 1, 7, 2, 1, 10, 8, 2, 1, 14, 19, 11, 1, 18, 40, 48, 7, 1, 23, 77, 154, 70, 5, 1, 28, 132, 421, 392, 71, 1, 34, 217, 1008, 1638, 690, 35, 1, 40, 340, 2210, 5623, 4548, 767, 16, 1, 47, 510, 4477, 16745, 22657, 8594, 566, 1, 54, 742, 8557, 44698, 92844, 64716, 11247, 226

Offset: 2

Andrew Howroyd, Feb 25 2023

Columns k >= 3 correspond to the 2-connected graphs.

Terms may be computed using the tools geng, vcolg and multig in nauty with some additional processing to check the degrees of nodes.

			Triangle begins:
  1;
  1,  2;
  1,  4;
  1,  7,   2;
  1, 10,   8,    2;
  1, 14,  19,   11;
  1, 18,  40,   48,     7;
  1, 23,  77,  154,    70,     5;
  1, 28, 132,  421,   392,    71;
  1, 34, 217, 1008,  1638,   690,    35;
  1, 40, 340, 2210,  5623,  4548,   767,    16;
  1, 47, 510, 4477, 16745, 22657,  8594,   566;
  1, 54, 742, 8557, 44698, 92844, 64716, 11247, 226;
  ...

Brendan McKay and Adolfo Piperno, nauty and Traces.

Column 2 is A014616.
Row sums are A360882.
Row sums except first column are A360871.
Cf. A046752, A322115, A360862, A360866.

A360868 Number of unlabeled connected loopless multigraphs with circuit rank n and degree >= 3 at each node.

Original entry on oeis.org

0, 1, 4, 23, 172, 1848, 25684

Offset: 1

Andrew Howroyd, Feb 25 2023

Diagonal sums of A360866.

Cf. A360864, A360867, A360879.

a(n) = Sum_{k>=1} A360866(n + k - 1, k).

cp's OEIS Frontend

A046752 Triangle read by rows: T(n,k) is the number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges on k nodes and degree >= 3 at each node, n >= 3, 2 <= k <= floor(2*n/3).

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A360867 Number of unlabeled connected loopless multigraphs with n edges and degree >= 3 at each node.

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A360862 Triangle read by rows: T(n,k) is the number of unlabeled connected multigraphs with n edges on k nodes and degree >= 3 at each node, loops allowed, n >= 2, 1 <= k <= floor(2*n/3).

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A360870 Triangle read by rows: T(n,k) is the number of unlabeled connected multigraphs with n edges on k nodes, no cut-points and degree >= 3 at each node, loops allowed, n >= 2, 1 <= k <= floor(2*n/3).

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A360868 Number of unlabeled connected loopless multigraphs with circuit rank n and degree >= 3 at each node.

Views

Author

Keywords

Crossrefs

Formula