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A001186 Number of cubic Hamiltonian graphs with 2n nodes. 1
1, 2, 5, 17, 80, 474, 3841, 39635, 495991, 7170657, 116171803, 2070451150, 40130198979, 839266928707, 18826133329753 (list; graph; refs; listen; history; text; internal format)



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.


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


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


Sequence in context: A243337 A259622 A054499 * A125282 A020125 A076322

Adjacent sequences:  A001183 A001184 A001185 * A001187 A001188 A001189




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


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



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Last modified October 7 17:44 EDT 2022. Contains 357275 sequences. (Running on oeis4.)