A006800 -id:A006800 - cp's OEIS frontend

A006799 Number of vertex-transitive graphs with n nodes.

1, 2, 2, 4, 3, 8, 4, 14, 9, 22, 8, 74, 14, 56, 48, 286, 36, 380, 60, 1214, 240, 816, 188, 15506, 464, 4236, 1434, 25850, 1182, 46308, 2192, 677402, 6768, 132580, 11150, 1963202, 14602, 814216, 48462, 13104170, 52488, 9462226, 99880, 39134640, 399420, 34333800, 364724

Offset: 1

N. J. A. Sloane

CRC Handbook of Combinatorial Designs, 1996, p. 649.
Brendan McKay, personal communication.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Nino Bašić, Martin Knor, and Riste Škrekovski, On regular graphs with Šoltés vertices, arXiv:2303.11996 [math.CO], 2023.
Derek Holt and Gordon Royle, A Census of Small Transitive Groups and Vertex-Transitive Graphs, arXiv:1811.09015 [math.CO], 2018.
B. D. McKay and G. F. Royle, The transitive graphs with at most 26 vertices, Ars Combin. 30 (1990), 161-176. (Annotated scanned copy)
Brendan D. McKay, Gordon F. Royle, The transitive graphs with at most 26 vertices, Ars Combin. 30 (1990), 161-176.
G. Royle, Transitive graphs
Steven Skiena, A Database of Graphs in Combinatorica Format.
Eric Weisstein's World of Mathematics, Vertex-Transitive Graph
Eric Weisstein's World of Mathematics, Cayley Graph

Row sums of A319367.

Cf. A006792, A006793, A006800, A185959.

Inverse Moebius transform of A006800. - Andrew Howroyd, Sep 18 2018

More terms from Vladeta Jovovic, Jun 30 2007

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

A319368 Triangle read by rows: T(n,k) is the number of simple connected vertex transitive graphs with n nodes and valency k, (0 <= k < n).

Original entry on oeis.org

1, 0, 1, 0, 0, 1, 0, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, 1, 2, 1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 0, 1, 2, 3, 2, 1, 1, 0, 0, 1, 0, 3, 0, 2, 0, 1, 0, 0, 1, 3, 3, 4, 3, 2, 1, 1, 0, 0, 1, 0, 2, 0, 2, 0, 1, 0, 1, 0, 0, 1, 4, 10, 12, 13, 11, 7, 4, 1, 1, 0, 0, 1, 0, 3, 0, 4, 0, 3, 0, 1, 0, 1

Offset: 1

Andrew Howroyd, Sep 17 2018

			Triangle begins:
  1;
  0, 1;
  0, 0, 1;
  0, 0, 1, 1;
  0, 0, 1, 0,  1;
  0, 0, 1, 2,  1,  1;
  0, 0, 1, 0,  1,  0,  1;
  0, 0, 1, 2,  3,  2,  1,  1;
  0, 0, 1, 0,  3,  0,  2,  0,  1;
  0, 0, 1, 3,  3,  4,  3,  2,  1,  1;
  0, 0, 1, 0,  2,  0,  2,  0,  1,  0,  1;
  0, 0, 1, 4, 10, 12, 13, 11,  7,  4,  1,  1;
  0, 0, 1, 0,  3,  0,  4,  0,  3,  0,  1,  0,  1;
  0, 0, 1, 3,  5,  6,  8,  9,  6,  6,  3,  2,  1,  1;
  0, 0, 1, 0,  7,  0, 12,  0, 12,  0,  8,  0,  3,  0, 1;
  0, 0, 1, 4, 13, 25, 39, 47, 48, 40, 27, 16,  7,  3, 1, 1;
  0, 0, 1, 0,  4,  0,  7,  0, 10,  0,  7,  0,  4,  0, 1, 0, 1;
  0, 0, 1, 5, 12, 23, 36, 45, 53, 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.

Row sums are A006800.

Cf. A319367.

T(n,k) = Sum_{d|n} moebius(n/d) * A319367(d,k).

A054917 Number of connected unlabeled vertex-transitive graphs with n nodes such that complement is also connected.

Original entry on oeis.org

1, 0, 0, 0, 1, 2, 2, 6, 5, 14, 6, 54, 12, 46, 40, 258, 34, 350, 58, 1166, 230, 798, 186, 15338, 458, 4206, 1416, 25734, 1180, 46164, 2190, 676830, 6750, 132506, 11138, 1962310, 14600, 814094, 48432, 13101722, 52486, 9461632, 99878, 39133004, 399310, 34333422, 364722

Offset: 1

N. J. A. Sloane, May 24 2000

nonn

V. A. Liskovets, Some easily derivable sequences, J. Integer Sequences, 3 (2000), #00.2.2.

Cf. A006799, A006800.

nmax = 47;
A006799 = Cases[Import["https://oeis.org/A006799/b006799.txt", "Table"], {, }][[All, 2]];
A006800 = Table[Sum[MoebiusMu[n/d] A006799[[d]], {d, Divisors[n]}], {n, 1, nmax}];
a[n_] := 2*A006800[[n]] - A006799[[n]];
Array[a, nmax] (* Jean-François Alcover, Aug 27 2019, after Andrew Howroyd *)

a(n) = 2*A006800(n) - A006799(n).

Missing a(1) inserted and a(32)-a(47) from Andrew Howroyd, Nov 27 2018

cp's OEIS Frontend

A006799 Number of vertex-transitive graphs with n nodes.

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A319368 Triangle read by rows: T(n,k) is the number of simple connected vertex transitive graphs with n nodes and valency k, (0 <= k < n).

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Formula

A054917 Number of connected unlabeled vertex-transitive graphs with n nodes such that complement is also connected.

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Mathematica

Formula

Extensions