A319372 -id:A319372 - cp's OEIS frontend

A319367 Triangle read by rows: T(n,k) is the number of simple vertex transitive graphs with n nodes and valency k, (0 <= k < n).

1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 2, 2, 1, 1, 1, 0, 1, 0, 1, 0, 1, 1, 1, 2, 3, 3, 2, 1, 1, 1, 0, 2, 0, 3, 0, 2, 0, 1, 1, 1, 2, 3, 4, 4, 3, 2, 1, 1, 1, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 1, 1, 4, 7, 11, 13, 13, 11, 7, 4, 1, 1, 1, 0, 1, 0, 3, 0, 4, 0, 3, 0, 1, 0, 1

Offset: 1

Andrew Howroyd, Sep 17 2018

			Triangle begins, n >= 1, 0 <= k < n:
  1;
  1, 1;
  1, 0, 1;
  1, 1, 1, 1;
  1, 0, 1, 0,  1;
  1, 1, 2, 2,  1,  1;
  1, 0, 1, 0,  1,  0,  1;
  1, 1, 2, 3,  3,  2,  1,  1;
  1, 0, 2, 0,  3,  0,  2,  0,  1;
  1, 1, 2, 3,  4,  4,  3,  2,  1,  1;
  1, 0, 1, 0,  2,  0,  2,  0,  1,  0,  1;
  1, 1, 4, 7, 11, 13, 13, 11,  7,  4,  1,  1;
  1, 0, 1, 0,  3,  0,  4,  0,  3,  0,  1,  0,  1;
  1, 1, 2, 3,  6,  6,  9,  9,  6,  6,  3,  2,  1,  1;
  1, 0, 3, 0,  8,  0, 12,  0, 12,  0,  8,  0,  3,  0, 1;
  1, 1, 3, 7, 16, 27, 40, 48, 48, 40, 27, 16,  7,  3, 1, 1;
  1, 0, 1, 0,  4,  0,  7,  0, 10,  0,  7,  0,  4,  0, 1, 0, 1;
  1, 1, 4, 7, 16, 24, 38, 45, 54, 54, 45, 38, 24, 16, 7, 4, 1, 1;
  ...

Andrew Howroyd, Table of n, a(n) for n = 1..496
B. D. McKay and G. F. Royle, The transitive graphs with at most 26 vertices, Ars Combin. 30 (1990), 161-176. (Annotated scanned copy)
Gordon Royle, Transitive Graphs.
Eric Weisstein's World of Mathematics, Vertex-Transitive Graph.

Columns k=2..12 (even n only for odd k) are A023645, A023646, A023647, A023640, A023641, A023642, A023643, A023644, A023637, A023638, A023639.
Row sums are A006799.
Cf. A319368, A319372.

A185959 Number of Cayley graphs on n nodes.

Original entry on oeis.org

1, 2, 2, 4, 3, 8, 4, 14, 9, 20, 8, 74, 14, 56, 44, 278, 36, 376, 60, 1132, 240, 816, 188, 15394, 464, 4104, 1434, 25784, 1182, 45184, 2192, 659232, 6768, 131660, 11144, 1959040, 14602, 814216, 48462, 13055904, 52488, 9461984, 99880, 39134544, 399126, 34333800, 364724

Offset: 1

Eric W. Weisstein, Feb 07 2011

First differs from A006799 at n = 10.

Derek Holt and Gordon Royle, A Census of Small Transitive Groups and Vertex-Transitive Graphs, arXiv:1811.09015 [math.CO], 2018.
G. Royle, Transitive graphs
Eric Weisstein's World of Mathematics, Cayley Graph

Row sums of A319372.

Cf. A006792, A006799.

A006792 = Join[Array[0&, 10], Cases[Import["https://oeis.org/A006792/b006792.txt", "Table"], {, }][[All, 2]]];
A006799 = Cases[Import["https://oeis.org/A006799/b006799.txt", "Table"], {, }][[All, 2]];
a[n_] := A006799[[n]] - A006792[[n+1]];
Array[a, 47] (* Jean-François Alcover, Sep 05 2019 *)

a(n) = A006799(n) - A006792(n).

a(32)-a(47) from Danny Rorabaugh, Nov 26 2018

A319374 Number of cubic Cayley graphs with 2n nodes.

Original entry on oeis.org

1, 2, 3, 2, 7, 3, 7, 7, 8, 3, 20, 4, 9, 11, 17, 4, 24, 5, 20, 15, 11, 5, 56, 10, 14, 20, 24, 6, 51, 7, 43, 16, 16, 16, 73, 8, 17, 20, 53, 8, 52, 9, 29, 34, 19, 9, 156, 16, 39, 21, 36, 10, 78, 24, 63, 25, 24, 11, 174, 12, 25, 46, 125, 23, 63, 13, 44, 26, 61, 13

Offset: 2

Andrew Howroyd, Sep 17 2018

nonn

First differs from A023646 at n=5.

G. Royle, Cubic transitive graphs

Column k=3 of A319372.

Cf. A023646, A241164.

Inverse Moebius transform of A241164.

cp's OEIS Frontend

A319367 Triangle read by rows: T(n,k) is the number of simple vertex transitive graphs with n nodes and valency k, (0 <= k < n).

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A185959 Number of Cayley graphs on n nodes.

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A319374 Number of cubic Cayley graphs with 2n nodes.

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