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A389263
Number of quartic graphs with minimal crossing number n and the minimal possible number of vertices.
3
1, 1, 1, 5, 1, 1, 14, 32, 1, 3, 1, 123, 9
OFFSET
0,4
COMMENTS
a(0) = 1 from the octahedral graph.
a(1) = 1 from the pentatope graph K_5.
a(2) = 1 from the co-(C4+C4) graph.
a(3) = 5 from Ci_9(1,3), GQ(2,1), and 3 others.
a(4) = 1 from K_4,4.
a(5) = 1 from Ci_10(1,4).
a(6) = 14 from the Chvatal graph, Ci_12(1,5), Qt23, and 11 others.
a(7) = 32 from the 13-cyclotomic graph and 31 others.
a(8) = 1 from Ci_12(2,3).
a(9) = 3 from Qt31 and 2 others.
a(10) = 1 from regular nonplanar diameter graph (4,2,14).
From Eric W. Weisstein, Apr 19 2026:
a(11) = 123 graphs.
a(12) = Qt44 and 8 others.
a(13) is not currently known.
a(14) = 1 graph.
LINKS
CROSSREFS
Cf. A389265 (number of nodes).
Cf. A307450 (cubic graphs).
Sequence in context: A144438 A157207 A008957 * A136267 A109960 A196019
KEYWORD
nonn,more
AUTHOR
Eric W. Weisstein, Sep 27 2025
EXTENSIONS
a(9)-a(10) from Eric W. Weisstein, Nov 07 2025
a(11)-a(12) from Eric W. Weisstein, Apr 19 2026
STATUS
approved