A033886 Number of connected 4-regular simple graphs on n vertices with girth at least 4.

1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 2, 2, 12, 31, 220, 1606, 16828, 193900, 2452818, 32670330, 456028474, 6636066099, 100135577747, 1582718912968

Offset: 0

Author

N. J. A. Sloane, Dec 17 2000

Keywords

• nonn
• nice
• more
• hard
• changed

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

Links

• Jason Kimberley, Connected regular graphs with girth at least 4.
• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g.
• Markus Meringer, Fast Generation of Regular Graphs and Construction of Cages, Journal of Graph Theory, Vol. 30, No. 2 (1999), 137-146.
• Markus Meringer, Tables of Regular Graphs.

Crossrefs

From Jason Kimberley, Mar 19 2010 and Jan 28 2011: (Start)

4-regular simple graphs with girth at least 4: this sequence (connected), A185244 (disconnected), A185344 (not necessarily connected).

Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), this sequence (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).

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)

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.