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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
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
A. E. Brouwer, The Heawood Graph
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.
Eric Weisstein's World of Mathematics, Smallest Cubic Crossing Number Graph
CROSSREFS
Cf. A110507.
Sequence in context: A351794 A065813 A076344 * A173686 A090975 A257579
KEYWORD
nonn,more
AUTHOR
Ed Pegg Jr, Apr 08 2019
STATUS
approved