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

Author

N. J. A. Sloane, Jan 24 2001

Keywords

• nonn
• nice

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."

Examples

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

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

Crossrefs

Cf. A005638, A002851, A032355, A091430.

Extensions

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