A001186 Number of cubic Hamiltonian graphs with 2n nodes.

1, 2, 5, 17, 80, 474, 3841, 39635, 495991, 7170657, 116171803, 2070451150, 40130198979, 839266928707, 18826133329753

Offset

2,2

References

McKay, Brendan D.; Royle, Gordon F.; Constructing the cubic graphs on up to 20 vertices. Thirteenth Australasian conference on combinatorial mathematics and computing (Sydney, 1985). Ars Combin. 21 (1986), A, 129-140.

Links

Table of n, a(n) for n=2..16.

F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, Computer investigations of cubic graphs, T.H.-Report 76-WSK-01, Technological University Eindhoven, Dept. Mathematics, 1976. [From N. J. A. Sloane, Jan 12 2012].

Jan Goedgebeur, Barbara Meersman, Carol T. Zamfirescu, Graphs with few Hamiltonian Cycles, arXiv:1812.05650 [math.CO], 2018.

R. J. Mathar, The Wigner 3n-j Graphs up to 12 Vertices, arXiv preprint arXiv:1109.2358 [math-ph], 2011-2012.

Roman Maurer, Counting small hamiltonian cubic graphs.

Roman Maurer, vega06.zip [substitute for the broken link above] [From R. J. Mathar, Sep 22 2010]

R. W. Pratt, The complete catalog of 3-regular diameter-3 planar graphs, Table 2 (1996)

Eric Weisstein's World of Mathematics, Cubic Graph

Eric Weisstein's World of Mathematics, Hamiltonian Graph

Eric Weisstein's World of Mathematics, LCF Notation

Formula

a(n) = A002851(n) - A164919(n). - R. J. Mathar, Sep 22 2010

Crossrefs

Sequence in context: A243337 A259622 A054499 * A125282 A020125 A076322

Adjacent sequences: A001183 A001184 A001185 * A001187 A001188 A001189

Keyword

nonn,hard,nice,more

Author

Martin Harborth (Martin.Harborth(AT)vt.siemens.de)

Extensions

a(11) from Vladeta Jovovic, Jul 02 2007

a(12) from Sean A. Irvine, Sep 25 2015

a(13) from Sean A. Irvine, Oct 06 2015

a(14)-a(16) from Jan Goedgebeur, Sep 07 2019

Status

approved