A006792 -id:A006792

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page 1

A045872

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

+20
0

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

10,6

LINKS

Table of n, a(n) for n=10..27.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane

STATUS

approved

A006799

Number of vertex-transitive graphs with n nodes.
(Formerly M0302)

+10
10

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

REFERENCES

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).

LINKS

Table of n, a(n) for n=1..47.

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

FORMULA

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

CROSSREFS

Row sums of A319367.

Cf. A006792, A006793, A006800, A185959.

KEYWORD

nonn,nice,hard

AUTHOR

N. J. A. Sloane

EXTENSIONS

More terms from Vladeta Jovovic, Jun 30 2007

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

STATUS

approved

A185959

Number of Cayley graphs on n nodes.

+10
7

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

First differs from A006799 at n = 10.

LINKS

Table of n, a(n) for n=1..47.

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

FORMULA

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

MATHEMATICA

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 *)

CROSSREFS

Row sums of A319372.

Cf. A006792, A006799.

KEYWORD

nonn,hard

AUTHOR

Eric W. Weisstein, Feb 07 2011

EXTENSIONS

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

STATUS

approved

A330697

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

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..66.

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)

PROG

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

CROSSREFS

Cf. A006792, A006799, A185959, A330698.

KEYWORD

nonn

AUTHOR

M. Farrokhi D. G., Dec 26 2019

STATUS

approved

A330698

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

+10
2

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..66.

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)