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

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

1,10

Comments

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."

References

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

Links

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

Example

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

Crossrefs

Cf. A005638, A002851, A032355, A091430.

Sequence in context: A078821 A125184 A236575 * A114591 A161849 A056175

Adjacent sequences: A059279 A059280 A059281 * A059283 A059284 A059285

Keyword

nonn,nice

Author

N. J. A. Sloane, Jan 24 2001

Extensions

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

Status

approved