A032355 -id:A032355 - cp's OEIS frontend

A234718 Indices of records in A032355 = number of connected transitive trivalent (or cubic) graphs with 2n nodes.

Original entry on oeis.org

2, 3, 5, 6, 9, 10, 12, 18, 24, 30, 48, 60, 72, 96, 120, 144, 192, 256, 288, 384, 512, 576

Offset: 1

M. F. Hasler, Apr 19 2014

nonn

See A234719 for the record values A032355(a(n)).

A032355(a(n)) > A032355(k) for all k < a(n).

A234719 Record values in A032355 = number of connected transitive trivalent (or cubic) graphs with 2n nodes.

Original entry on oeis.org

1, 2, 3, 4, 5, 7, 11, 12, 32, 38, 90, 105, 124, 274, 303, 411, 988, 1061, 1417, 3701, 4485, 5692

Offset: 1

M. F. Hasler, Apr 19 2014

nonn

See A234718 for the indices k=A234718(n) of the records a(n) = A032355(k).

a(n) = A032355(A234718(n)) > A032355(k) for all k < A234718(n).

A059282 Number of symmetric trivalent (or cubic) connected graphs on 2n nodes (the Foster census).

Original entry on oeis.org

0, 1, 1, 1, 1, 0, 1, 1, 1, 2, 0, 1, 1, 1, 1, 1, 0, 0, 1, 1, 1, 0, 0, 1, 1, 0, 1, 3, 0, 1, 1, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 0, 1, 0, 0, 2, 2, 0, 1, 1, 0, 1, 1, 3, 1, 0, 0, 2, 1, 0, 1, 2, 0, 0, 1, 0, 0, 0, 0, 2, 1, 0, 1, 1, 0, 0, 1, 0, 3, 0, 0, 6, 0, 0, 0, 0, 0, 0, 4, 0, 1, 0, 0, 3, 1, 0, 0, 1, 0, 1, 1, 1, 0, 0, 0, 3, 1, 3, 1, 3, 0, 0, 0, 0, 2, 0, 0, 3, 1, 0, 0, 1, 1, 0, 1, 4, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 2, 0, 0, 2, 1, 0, 0, 1

Offset: 1

N. J. A. Sloane, Jan 24 2001

Potočnik et al. refer to these as arc-transitive connected cubic vertex-transitive graphs.

Marston Conder (Email to N. J. A. Sloane, May 08 2017) remarks that "the first 5000 terms of A091430 are the same as the first 5000 terms of this sequence, with the exception of the 5th and 14th terms (corresponding to the Petersen graph and the Coxeter graph). I verified this soon after completing the determination of all connected symmetric 3-valent graphs of order up to 10000, in June 2011."

			The first example is K_4 with 4 nodes, thus a(2) = 1.

I. Z. Bouwer, W. W. Chernoff, B. Monson and Z. Star, The Foster Census (Charles Babbage Research Centre, 1988), ISBN 0-919611-19-2.

Marston Conder, Table of n, a(n) for n = 1..5000 [The first 640 terms were added by N. J. A. Sloane, based on the work of Primož Potočnik, Pablo Spiga and Gabriel Verret]
Marston Conder, Home Page (Contains tables of regular maps, hypermaps and polytopes, trivalent symmetric graphs, and surface actions)
Marston Conder, Trivalent (cubic) symmetric graphs on up to 10000 vertices
Marston Conder and P. Dobcsányi, Trivalent symmetric graphs on up to 768 vertices, J. Combinatorial Mathematics & Combinatorial Computing 40 (2002), 41-63.
Primož Potočnik, Pablo Spiga and Gabriel Verret, A census of small connected cubic vertex-transitive graphs (See the sub-page Table.html) [Broken link]
Gordon Royle et al., Cubic symmetric graphs (The Foster Census) [Broken link]
Gordon Royle, Cubic transitive graphs
Eric Weisstein's World of Mathematics, Cubic Symmetric Graph

Cf. A005638, A002851, A032355, A091430.

Updated all links. Corrected entries based on the Potočnik et al. table. - N. J. A. Sloane, Apr 19 2014

A241164 Number of 2n-vertex connected cubic vertex-transitive graphs which are Cayley graphs.

Original entry on oeis.org

1, 2, 2, 2, 4, 3, 4, 5, 5, 3, 11, 4, 5, 7, 10, 4, 12, 5, 10, 10, 7, 5, 32, 8, 9, 13, 13, 6, 30, 7, 26, 11, 11, 11, 36, 8, 11, 14, 29, 8, 27, 9, 16, 18, 13, 9, 90, 13, 23, 15, 20, 10, 41, 19, 35, 18, 17, 11, 100, 12, 17, 26, 82, 17, 35, 13

Offset: 2

N. J. A. Sloane, Apr 19 2014

nonn

N. J. A. Sloane, Table of n, a(n) for n = 2..640, based on the work of Primož Potočnik, Pablo Spiga and Gabriel Verret
Primož Potočnik, Pablo Spiga and Gabriel Verret, A census of small connected cubic vertex-transitive graphs (see the sub-page Table.html)
G. Royle, Cubic transitive graphs

Cf. A032355, A185959.

A241163 Maximal girth of a connected transitive trivalent (or cubic) graph with 2n nodes.

Original entry on oeis.org

3, 4, 4, 5, 4, 6, 6, 6, 6, 6, 6, 7, 7, 8, 6, 7, 7, 6, 8, 8, 6, 6, 8, 8, 8, 8, 8, 8, 9, 6, 8, 8, 8, 8, 8, 8, 6, 8, 10, 8, 8, 6, 6, 10, 6, 6, 10, 7, 10, 9, 8, 8, 10, 10, 10, 8, 8, 6, 10, 8, 6, 10, 10, 8, 10, 6, 8, 8, 10, 6, 10, 8, 8, 8, 6, 8, 10, 6, 10, 12, 8, 6, 12, 8, 6, 8, 10, 8, 10, 12, 6, 8, 6, 8, 12, 8, 10, 8, 10, 8, 12, 6, 10, 10, 8, 6, 12, 8, 10, 8, 12, 8, 10, 8, 8, 12, 6, 8, 12, 8, 8, 8, 6, 11, 10, 6, 12, 8, 10

Offset: 2

N. J. A. Sloane, Apr 19 2014

nonn

N. J. A. Sloane, Table of n, a(n) for n = 2..640, based on the work of Primož Potočnik, Pablo Spiga and Gabriel Verret
Primož Potočnik, Pablo Spiga and Gabriel Verret, A census of small connected cubic vertex-transitive graphs (See the sub-page Table.html)

Cf. A032355

A241167 Number of (not necessarily connected) vertex-transitive cubic graphs on 2n nodes.

Original entry on oeis.org

0, 1, 2, 3, 5, 10, 12, 23, 35, 56, 79, 137, 186, 293, 437, 647, 929, 1412, 1982, 2929, 4180, 6021, 8487, 12263, 17086, 24252, 33948, 47617, 66001, 92399, 127095, 176216, 242135, 333021, 454704, 623210, 846217, 1152111, 1560276, 2112523, 2846427, 3840117, 5151854, 6916122, 9250482, 12363845, 16470710

Offset: 1

N. J. A. Sloane, Apr 20 2014

nonn

EULER transform of A032355 = 0,1,2,2,3,4,3,4,...

Cf. A032355.

cp's OEIS Frontend

A234718 Indices of records in A032355 = number of connected transitive trivalent (or cubic) graphs with 2n nodes.

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A234719 Record values in A032355 = number of connected transitive trivalent (or cubic) graphs with 2n nodes.

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A059282 Number of symmetric trivalent (or cubic) connected graphs on 2n nodes (the Foster census).

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A241164 Number of 2n-vertex connected cubic vertex-transitive graphs which are Cayley graphs.

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A241163 Maximal girth of a connected transitive trivalent (or cubic) graph with 2n nodes.

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A241167 Number of (not necessarily connected) vertex-transitive cubic graphs on 2n nodes.

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