A006792 -id:A006792 - cp's OEIS frontend

A045872 a(n) = A006792(n)/2.

1, 0, 0, 0, 0, 2, 4, 0, 2, 0, 41, 0, 0, 0, 56, 0, 66, 0

Offset: 10

nonn

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

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

A330697 Numbers k such that every vertex-transitive graph of order k is a Cayley-graph.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 12, 13, 14, 17, 19, 21, 22, 23, 25, 27, 29, 31, 33, 37, 38, 39, 41, 43, 46, 47, 49, 53, 55, 59, 61, 62, 67, 69, 71, 73, 79, 83, 86, 87, 89, 93, 94, 95, 97, 101, 103, 107, 109, 113, 115, 118, 121, 123, 125, 127, 129, 131, 133, 134, 137, 139

Offset: 1

M. Farrokhi D. G., Dec 26 2019

nonn

Numbers k for which A185959(k) = A006799(k).
Numbers k for which A006792(k) = 0.
In the Farrokhi reference, a Cayley number is a number k such that all vertex transitive graphs of order k are Cayley graphs.

M. Farrokhi D. G., List of known Cayley numbers less than or equal to 1000000
M. Farrokhi D. G., Cayley numbers
M. Farrokhi D. G., Cayley numbers (GitHub)

Cf. A006792, A006799, A185959, A330698.

# See M. Farrokhi Github repository for a GAP program.

A330698 Numbers k such that there exists a non-Cayley vertex-transitive graph of order k.

Original entry on oeis.org

10, 15, 16, 18, 20, 24, 26, 28, 30, 32, 34, 35, 36, 40, 42, 44, 45, 48, 50, 51, 52, 54, 56, 57, 58, 60, 63, 64, 65, 66, 68, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 88, 90, 91, 92, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 111, 112, 114, 116, 117, 119, 120, 122, 124

Offset: 1

M. Farrokhi D. G., Dec 26 2019

nonn

Numbers k for which A185959(k) < A006799(k).
Numbers k for which A006792(k) <> 0.
In the Farrokhi reference, a Cayley number is a number k such that all vertex transitive graphs of order k are Cayley graphs.

M. Farrokhi D. G., List of known non-Cayley numbers less than or equal to 1000000
M. Farrokhi D. G., Cayley numbers
M. Farrokhi D. G., Cayley numbers (GitHub)

Cf. A006792, A006799, A185959, A330697.

A327754 Number of connected Cayley graphs on n nodes.

Original entry on oeis.org

1, 1, 1, 2, 2, 5, 3, 10, 7, 16, 7, 64, 13, 51, 40, 264, 35, 361, 59, 1110, 235, 807, 187, 15310, 461, 4089, 1425, 25726, 1181, 45118, 2191

Offset: 1

M. Farrokhi D. G., Sep 24 2019

Gordon Royle, Transitive Graphs

Cf. A185959, A006799, A006792.

cp's OEIS Frontend

A045872 a(n) = A006792(n)/2.

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A006799 Number of vertex-transitive graphs with n nodes.

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A185959 Number of Cayley graphs on n nodes.

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A330697 Numbers k such that every vertex-transitive graph of order k is a Cayley-graph.

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GAP

A330698 Numbers k such that there exists a non-Cayley vertex-transitive graph of order k.

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A327754 Number of connected Cayley graphs on n nodes.

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