A325447
Triangle read by rows: T(n,k) is the number of simple nonseparable (or 2-connected) graphs on n unlabeled nodes with circumference k, (n >= 3, k >= 3).
Original entry on oeis.org
1, 0, 3, 0, 2, 8, 0, 2, 6, 48, 0, 2, 9, 74, 383, 0, 2, 10, 159, 756, 6196, 0, 2, 13, 276, 2058, 14634, 177083, 0, 2, 14, 505, 4824, 48137, 384942, 9305118
Offset: 3
Triangle begins, (n >= 3, k >= 3):
1;
0, 3;
0, 2, 8;
0, 2, 6, 48;
0, 2, 9, 74, 383;
0, 2, 10, 159, 756, 6196;
0, 2, 13, 276, 2058, 14634, 177083;
0, 2, 14, 505, 4824, 48137, 384942, 9305118;
...
A243321
Number of simple connected graphs with n nodes that are bipartite and planar.
Original entry on oeis.org
1, 1, 1, 3, 5, 16, 41, 158, 582, 2749, 13852, 80341, 503582, 3419670, 24533162, 184227017
Offset: 1
-
A164099 = Cases[Import["https://oeis.org/A164099/b164099.txt", "Table"], {, }][[All, 2]];
(* EulerInvTransform is defined in A022562 *)
EulerInvTransform[{0} ~Join~ A164099 + 1] (* Jean-François Alcover, Dec 03 2019, updated Mar 17 2020 *)
a(11)-a(16) added using tinygraph by
Falk Hüffner, May 10 2019
A243270
Number of unlabeled simple graphs with n nodes that are Hamiltonian and bipartite.
Original entry on oeis.org
1, 0, 0, 1, 0, 4, 0, 24, 0, 473, 0, 30512, 0, 6374556
Offset: 1
a(11)-a(14) added using tinygraph by
Falk Hüffner, Aug 13 2017
A243271
Number of unlabeled simple graphs with n nodes that are Hamiltonian and distance-regular.
Original entry on oeis.org
1, 0, 1, 2, 2, 4, 2, 5, 4, 6
Offset: 1
A243272
Number of unlabeled simple graphs with n nodes that are Hamiltonian and Eulerian.
Original entry on oeis.org
1, 0, 1, 1, 2, 5, 21, 120, 1312, 26525, 1073690, 84471633
Offset: 1
a(10)-a(11) added using tinygraph by
Falk Hüffner, Aug 15 2017
A243273
Number of unlabeled simple graphs with n nodes that are Hamiltonian and integral.
Original entry on oeis.org
0, 0, 0, 1, 7, 43, 379, 6185, 177071, 9305068
Offset: 1
A243274
Number of graphs with n nodes that are Hamiltonian and non-integral.
Original entry on oeis.org
1, 0, 1, 2, 1, 5, 4, 11, 12, 50
Offset: 1
A243275
Number of graphs with n nodes that are Hamiltonian and triangle-free.
Original entry on oeis.org
1, 0, 0, 1, 1, 4, 5, 35, 130, 1293, 13529, 232852, 5009335, 147950020
Offset: 1
Cf.
A003216 (Hamiltonian graphs),
A024607 (connected triangle-free graphs).
a(11)-a(14) added using tinygraph by
Falk Hüffner, Aug 15 2017
A243276
Number of graphs with n nodes that are Hamiltonian and have no induced subgraph isomorphic to K_4.
Original entry on oeis.org
1, 0, 1, 2, 5, 29, 188, 2481, 52499, 1857651, 104392105
Offset: 1
Cf.
A003216 (Hamiltonian graphs),
A079574 (connected K_4 free graphs).
A243319
Number of simple connected graphs with n nodes that are bipartite and distance regular.
Original entry on oeis.org
1, 1, 0, 1, 0, 2, 0, 3, 0, 3
Offset: 1
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