A243247
Number of unlabeled, connected graphs on n vertices with at least one subgraph isomorphic to an open-bowtie graph.
Original entry on oeis.org
0, 0, 0, 0, 10, 78, 755, 10709, 259123, 11703831, 1006591916, 164058548700, 50335887082115
Offset: 1
n=5: The ten simple (no loop) graphs satisfying the cricket (open bowtie) subgraph condition have vertex degrees: 4^5, 4^3 3^2, 4^2 3^2 2, 4^2 2^3, 4 3^4, 4 3^3 1, 4 3^2 2^2, 4 3 2^2 1, 4 2^4 (bowtie), 4 2^2 1^2 (cricket). - _Wolfdieter Lang_, Jun 08 2025
a(11)-a(13) added using formula by
Falk Hüffner, Jan 16 2016
A243789
Number of simple connected graphs with n nodes that have no subgraph isomorphic to the open-bowtie graph or the diamond graph.
Original entry on oeis.org
1, 1, 2, 4, 9, 30, 89, 379, 1864, 12365, 106951, 1272286, 20722347
Offset: 1
a(11)-a(13) added using tinygraph by
Falk Hüffner, Sep 23 2020
A243790
Number of simple connected graphs with n nodes that are Hamiltonian and have no subgraph isomorphic to the open-bowtie graph.
Original entry on oeis.org
1, 0, 1, 3, 3, 9, 13, 59, 203, 1651, 15728
Offset: 1
A243791
Number of simple connected graphs with n nodes that are Eulerian and have no subgraph isomorphic to the open-bowtie graph.
Original entry on oeis.org
1, 0, 1, 1, 1, 2, 3, 8, 19, 62
Offset: 1
A243792
Number of simple connected graphs with n nodes that are integral and have no subgraph isomorphic to the open-bowtie graph.
Original entry on oeis.org
1, 1, 1, 2, 1, 4, 1, 3, 0, 15
Offset: 1
A243793
Number of simple connected graphs with n nodes that are not integral and have no subgraph isomorphic to the open-bowtie graph.
Original entry on oeis.org
0, 0, 1, 4, 10, 30, 97, 405, 1957, 12725
Offset: 1
A243794
Number of simple connected graphs with n nodes that are planar and have no subgraph isomorphic to the open-bowtie graph.
Original entry on oeis.org
1, 1, 2, 6, 11, 33, 94, 370, 1627, 8895, 56416, 414456, 3382661
Offset: 1
a(11)-a(13) added using tinygraph by
Falk Hüffner, May 12 2019
A243795
Number of simple connected graphs with n nodes that have no subgraph isomorphic to the open-bowtie graph or the bull graph.
Original entry on oeis.org
1, 1, 2, 6, 7, 22, 65, 285, 1442, 10106, 92277, 1153548, 19504515
Offset: 1
a(11)-a(13) added using tinygraph by
Falk Hüffner, Sep 23 2020
A243799
Number of connected graphs with n nodes that are chordal and are open-bowtie free.
Original entry on oeis.org
1, 1, 2, 5, 6, 13, 25, 58, 130, 316, 769, 1962, 5052, 13342, 35629, 96671
Offset: 1
Definition corrected (connected only) by
Falk Hüffner, Jul 01 2018
a(11)-a(16) added using tinygraph by
Falk Hüffner, Jul 01 2018
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