|
|
A033886
|
|
Number of connected 4-regular simple graphs on n vertices with girth at least 4.
|
|
20
|
|
|
1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 12, 31, 220, 1606, 16828, 193900, 2452818, 32670330, 456028474, 6636066099, 100135577747, 1582718912968
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,11
|
|
COMMENTS
|
The null graph on 0 vertices is vacuously connected and 4-regular; since it is acyclic, it has infinite girth. - Jason Kimberley, Jan 29 2011
|
|
REFERENCES
|
M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), pp. 137-146.
|
|
LINKS
|
|
|
CROSSREFS
|
4-regular simple graphs with girth at least 4: this sequence (connected), A185244 (disconnected), A185344 (not necessarily connected).
Connected 4-regular simple graphs with girth at least g: A006820 (g=3), this sequence (g=4), A058343 (g=5), A058348 (g=6).
Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)
|
|
KEYWORD
|
nonn,nice,more,hard
|
|
AUTHOR
|
|
|
EXTENSIONS
|
By running M. Meringer's GENREG at U. Newcastle for 6.25, 107 and 1548 processor days, a(21), a(22), and a(23) were completed by Jason Kimberley on Dec 06 2009, Mar 19 2010, and Nov 02 2011.
|
|
STATUS
|
approved
|
|
|
|