A006791 - OEIS

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A006791

Number of cyclically-5-connected planar trivalent graphs with 2n nodes.
(Formerly M2373)

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

10,5

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

Table of n, a(n) for n=10..38.

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.

Sequence in context: A240737 A075223 A071332 * A111358 A111357 A081621

Adjacent sequences: A006788 A006789 A006790 * A006792 A006793 A006794

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved