A372169 Number of unlabeled triangle-free graphs covering n vertices.

1, 0, 1, 1, 4, 7, 24, 69, 303, 1487, 10275, 92899, 1157109, 19534822, 447074367, 13764681083, 567227701549, 31139379910949

Offset

0,5

Comments

The labeled version is A372168.

Links

Table of n, a(n) for n=0..17.

Eric Weisstein's World of Mathematics, Triangle-Free Graph

Gus Wiseman, The a(6) = 24 unlabeled triangle-free graphs covering 6 vertices.

Formula

First differences of A006785.

Example

Non-isomorphic representatives of the a(5) = 7 graphs:
  12-35-45
  13-24-35-45
  14-25-35-45
  15-25-35-45
  12-13-24-35-45
  15-23-24-35-45
  13-14-23-24-35-45

Crossrefs

Dominated by A002494, labeled A006129.

Covering case of A006785, labeled A213434.

The connected case is A024607.

For all cycles (not just triangles) we have A144958, labeled A105784.

The labeled version is A372168.

For a unique triangle (labeled) we have A372171, non-covering A372172.

Column k = 0 of A372173, labeled A372167.

For a unique triangle (unlabeled) we have A372174, non-covering A372194.

A001858 counts acyclic graphs, unlabeled A005195.

A006125 counts simple graphs, unlabeled A000088.

A054548 counts covering graphs by number of edges, unlabeled A370167.

A372170 counts graphs by triangles, unlabeled A263340.

Cf. A000055, A000272, A053530, A121251, A322700, A372175, A372191.

Sequence in context: A143608 A079441 A129418 * A073218 A276288 A219700

Adjacent sequences: A372166 A372167 A372168 * A372170 A372171 A372172

Keyword

nonn,more

Author

Gus Wiseman, Apr 23 2024

Status

approved