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A307450 Number of cubic graphs with minimal crossing number n and the minimal possible number of vertices. 1
1, 1, 2, 8, 2, 2, 3, 4, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(0) = 1 from the complete graph K_4.

a(1) = 1 from the utility graph K_{3,3}.

a(2) = 2 from the Petersen graph (and 1 other).

a(3) = 8 from the Heawood graph, GP(7,2) (and 6 others).

a(4) = 2 from the Moebius-Kantor and 8-crossed prism graphs.

a(5) = 2 from the Pappus graph (and 1 other).

a(6) = 3 from the Desargues graph (and 2 others based on 10_3 configurations).

a(7) = 4 from the 7-crossing graphs (4 in total).

a(8) = 3 from the McGee and Nauru graphs (and 1 other).

a(9) >= 3 from GP(13,5), the Coxeter-1, and McGee+1 graphs (and unknown others). - Eric W. Weisstein, Apr 12 2019

a(10) >= 2 from the Levi-1 (=McGee+2) graph and graph from 2019 Clancy et al. preprint (and unknown others). - Eric W. Weisstein, Apr 12 2019

a(11) >= 1 from the Coxeter graph (and unknown others).

a(13) >= 1 from the Levi graph (and unknown others).

LINKS

Table of n, a(n) for n=0..8.

A. E. Brouwer, The Heawood Graph

Geoff Exoo, Rectilinear Drawings of Famous Graphs

Michael Haythorpe and Alex Newcombe, There are no Cubic Graphs on 26 Vertices with Crossing Number 11, arXiv preprint arXiv:1804.10336 [math.CO], 2018.

Ed Pegg, Jr., Cubic Symmetric Graphs

Ed Pegg, Jr., Cubic Symmetric Graphs

Ed Pegg, Jr., Heawood graph shown with crossing number 3 and more symmetrically

Eric Weisstein's World of Mathematics, Smallest Cubic Crossing Number Graph

CROSSREFS

Cf. A110507.

Sequence in context: A194567 A065813 A076344 * A173686 A090975 A257579

Adjacent sequences:  A307447 A307448 A307449 * A307451 A307452 A307453

KEYWORD

nonn,more

AUTHOR

Ed Pegg Jr, Apr 08 2019

STATUS

approved

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Last modified January 23 22:36 EST 2020. Contains 331177 sequences. (Running on oeis4.)