A164919 Number of simple connected cubic nonhamiltonian graphs on 2n nodes.

0, 0, 0, 0, 2, 5, 35, 219, 1666, 14498, 148790, 1768732, 24029714, 366939032, 6213299362, 115388854837

Offset

1,5

Links

Table of n, a(n) for n=1..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:1109.2358, 2011

Eric Weisstein's World of Mathematics, Cubic Nonhamiltonian Graph

Example

The only simple connected cubic nonhamiltonian graphs on 10 nodes are the Petersen graph and the graph with two copies of K4 with one edge subdivided, and the two subdivision vertices connected by a bridge. - Falk Hüffner, May 21 2026

Crossrefs

Sequence in context: A000665 A058882 A000659 * A272678 A063443 A133473

Adjacent sequences: A164916 A164917 A164918 * A164920 A164921 A164922

Keyword

nonn,more

Author

Eric W. Weisstein, Aug 31 2009

Extensions

Two more values (subtracting A002851 and A001186) from R. J. Mathar, Sep 22 2010

a(11)-a(15) added by Jan Goedgebeur, Sep 07 2019

Offset corrected by Falk Hüffner, May 21 2026

Status

approved