A352216
Largest number of maximal diamond-free node-induced subgraphs of an n-node graph.
Original entry on oeis.org
1, 1, 1, 4, 7, 11, 21, 36, 62
Offset: 1
All graphs with at most three nodes are diamond-free, so a(n) = 1 for n <= 3 and any graph is optimal.
For 4 <= n <= 9, the following are all optimal graphs, i.e., graphs that have n nodes and a(n) maximal diamond-free subgraphs:
n = 4: the diamond graph;
n = 5: the wheel graph;
n = 6: the complement of the H graph, the complement of P_3 + P_3 (the disjoint union of two paths of length 2), and the octahedral graph;
n = 7: the complement of P_3 + P_4;
n = 8: the complement of P_3 + C_5, and the complement of 2*P_4;
n = 9: the complement of P_4 + C_5.
For a list of related sequences, see cross-references in
A342211.
A243250
Number of unlabeled, connected graphs on n vertices with at least one subgraph isomorphic to a diamond graph.
Original entry on oeis.org
0, 0, 0, 2, 10, 73, 688, 10150, 253396, 11629559
Offset: 1
A243560
Number of simple connected graphs with n nodes that are Hamiltonian and have no subgraph isomorphic to diamond graph.
Original entry on oeis.org
1, 0, 1, 1, 2, 9, 27, 190, 1750, 25658, 531204
Offset: 1
A243561
Number of simple connected graphs with n nodes that are distance regular and have no subgraph isomorphic to diamond graph.
Original entry on oeis.org
1, 1, 1, 1, 1, 2, 1, 3, 2, 4
Offset: 1
A243562
Number of simple connected graphs with n nodes that are Eulerian and have no subgraph isomorphic to diamond graph.
Original entry on oeis.org
1, 0, 1, 1, 2, 3, 8, 21, 79, 334, 2190
Offset: 1
A243563
Number of simple connected graphs with n nodes that are non-integral and have no subgraph isomorphic to diamond graph.
Original entry on oeis.org
0, 0, 1, 3, 10, 35, 162, 964, 7682, 86994
Offset: 1
A243564
Number of simple connected graphs with n nodes that are integral and have no subgraph isomorphic to diamond graph.
Original entry on oeis.org
1, 1, 1, 1, 1, 4, 3, 3, 2, 18
Offset: 1
A243565
Number of simple connected graphs with n nodes that are planar and have no subgraph isomorphic to diamond graph.
Original entry on oeis.org
1, 1, 2, 4, 11, 38, 159, 882, 6242, 55316, 578130, 6774786
Offset: 1
a(11)-a(12) added using tinygraph by
Falk Hüffner, May 09 2019
A243567
Number of simple connected graphs with n nodes that are have no subgraph isomorphic to diamond graph or the bowtie graph.
Original entry on oeis.org
1, 1, 2, 4, 10, 36, 141, 784, 5626, 56249, 774266, 14750595
Offset: 1
a(11)-a(12) added using tinygraph by
Falk Hüffner, Sep 23 2020
A243568
Number of simple connected graphs with n nodes that are have no subgraph isomorphic to diamond graph or the bull graph.
Original entry on oeis.org
1, 1, 2, 4, 9, 26, 80, 340, 1690, 11432, 101142, 1228608, 20329150
Offset: 1
a(11)-a(13) added using tinygraph by
Falk Hüffner, Sep 23 2020
Showing 1-10 of 11 results.
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