A006791 Number of cyclically-5-connected planar trivalent graphs with 2n nodes.

1, 0, 1, 1, 3, 4, 12, 23, 71, 187, 627, 1970, 6833, 23384, 82625, 292164, 1045329, 3750277, 13532724, 48977625, 177919099, 648145255, 2368046117, 8674199554, 31854078139, 117252592450, 432576302286, 1599320144703, 5925181102878

Offset: 10

Author

N. J. A. Sloane

Keywords

• nonn

Comments

This sequence and A111358 are the same sequence. The correspondence is just that these objects are planar duals of each other. But the offset and step are different: if the cubic graph has 2*n vertices, the dual triangulation has n+2 vertices. - Brendan McKay, May 24 2017

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• D. A. Holton and B. D. McKay, The smallest non-hamiltonian 3-connected cubic planar graphs have 38 vertices, J. Combinat. Theory B vol 45, iss. 3 (1988) 305-319.
• D. A. Holton and B. D. McKay, Erratum, J. Combinat. Theory B vol 47, iss. 2 (1989) 248.
• B. McKay, Email to N. J. A. Sloane, Jul. 1991
• Irene Pivotto, Gordon Royle, Highly-connected planar cubic graphs with few or many Hamilton cycles, arXiv:1901.10683 [math.CO], 2019.

Crossrefs

Cf. A111358.