A372191 Number of unlabeled simple graphs covering n vertices with a unique undirected cycle of length > 2.

0, 0, 0, 1, 2, 6, 16

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(3) = 1 through a(6) = 16 covering graphs with a unique cycle.

Formula

First differences of A372192.

Crossrefs

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

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

The non-covering version is A372192, labeled A372193.

The labeled version is A372195, column k = 1 of A372175.

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, A370169.

Sequence in context: A302775 A181993 A123475 * A193341 A009711 A009586

Adjacent sequences: A372188 A372189 A372190 * A372192 A372193 A372194

Keyword

nonn,more,new

Author

Gus Wiseman, Apr 27 2024

Status

approved