|
|
A179184
|
|
Number of connected 2-regular simple graphs with n vertices.
|
|
13
|
|
|
1, 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, 1, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0
|
|
COMMENTS
|
All simple graphs have girth at least 3. Acyclic graphs have infinite girth.
|
|
LINKS
|
|
|
FORMULA
|
a(0)=1; for 0<n<3 a(n)=0; for n>=3 , a(n)=1.
Proof: The null graph is vacuously 2-regular. There are no 2-regular simple graphs with 1 or 2 vertices. The n-cycle has girth n. QED.
|
|
PROG
|
(Magma) [1, 0, 0, 1^^97];
|
|
CROSSREFS
|
2-regular simple graphs (with girth at least 3): this sequence (connected), A165652 (disconnected), A008483 (not necessarily connected).
2-regular connected: this sequence (simple graphs), A000012 (multigraphs with loops allowed).
Connected regular simple graphs: A005177 (any degree), A068934 (triangular array), specified degree k: this sequence (k=2), A002851 (k=3), A006820 (k=4),A006821 (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), A014381 (k=9), A014382 (k=10), A014384 (k=11).
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|