A185117 Number of connected 2-regular simple graphs on n vertices with girth at least 7.

1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset

0

Links

Table of n, a(n) for n=0..101.

Jason Kimberley, Connected regular graphs with girth at least 7

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

Formula

a(0)=1; for 0<n<7 a(n)=0; for n>=7 , a(n)=1.

This sequence is the inverse Euler transformation of A185327.

Example

The null graph is vacuously 2-regular and, being acyclic, has infinite girth.
There are no 2-regular simple graphs with 1 or 2 vertices.
The n-cycle has girth n.

Crossrefs

2-regular simple graphs with girth at least 7: this sequence (connected), A185227 (disconnected), A185327 (not necessarily connected).

Connected k-regular simple graphs with girth at least 7: A186727 (any k), A186717 (triangle); specific k: this sequence (k=2), A014375 (k=3).

Connected 2-regular simple graphs with girth at least g: A179184 (g=3), A185114 (g=4), A185115 (g=5), A185116 (g=6), this sequence (g=7), A185118 (g=8), A185119 (g=9).

Connected 2-regular simple graphs with girth exactly g: A185013 (g=3), A185014 (g=4), A185015 (g=5), A185016 (g=6), A185017 (g=7), A185018 (g=8).

Sequence in context: A205808 A238897 A297199 * A014045 A015269 A016347

Adjacent sequences: A185114 A185115 A185116 * A185118 A185119 A185120

Keyword

nonn,easy

Author

Jason Kimberley, Jan 28 2011

Status

approved