A372192 Number of unlabeled simple graphs on n vertices with a unique undirected cycle of length > 2.

0, 0, 0, 1, 3, 9, 25

Offset

0,5

Comments

An undirected cycle in a graph is a sequence of distinct vertices, up to rotation and reversal, such that there are edges between all consecutive elements, including the last and the first.

Links

Table of n, a(n) for n=0..6.

Gus Wiseman, The a(6) = 24 graphs with a unique cycle.

Formula

Partial sums of A372191.

Crossrefs

For no cycles we have A005195 (covering A144958), labeled A001858 (covering A105784).

The covering version is A372191, labeled A372195.

The labeled version is A372193.

Counting triangles instead of cycles gives A372194 (covering A372174), labeled A372172 (covering A372171).

A002807 counts cycles in a complete graph.

A006125 counts graphs, unlabeled A000088.

A006129 counts covering graphs, unlabeled A002494.

A372167 counts graphs by triangles, non-covering A372170.

A372173 counts unlabeled graphs by triangles (non-covering A263340).

A372176 counts labeled graphs by directed cycles.

Cf. A000055, A137916, A137917, A137918, A140637, A370167, A372169.

Sequence in context: A148920 A351937 A204448 * A032681 A293852 A005209

Adjacent sequences: A372189 A372190 A372191 * A372193 A372194 A372195

Keyword

nonn,more

Author

Gus Wiseman, Apr 27 2024

Status

approved