A058348 Number of connected 4-regular simple graphs on n vertices with girth at least 6.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 4, 0, 19, 0, 1272, 25, 494031, 13504

Offset: 0

Author

N. J. A. Sloane, Dec 17 2000

Keywords

• nonn
• more
• hard

Comments

From Jason Kimberley, 2011: (Start)

The null graph on 0 vertices is vacuously connected and 4-regular; since it is acyclic, it has infinite girth.

Does a(2n+1) ever exceed a(2n)?

(End)

Links

• Jason Kimberley, Connected regular graphs with girth at least 6
• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
• M. Meringer, Tables of Regular Graphs
• M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146. [_Jason Kimberley_, Jan 29 2011]

Crossrefs

From Jason Kimberley, Jan 29 2011: (Start)

Connected k-regular simple graphs with girth at least 6: A186726 (any k), A186716 (triangle); specified degree k: A185116 (k=2), A014374 (k=3), this sequence (k=4).

Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), A058343 (g=5), this sequence (g=6).

Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)

Extensions

Jason Kimberley inserted Meringer's computed terms a(n)=0 for n in [27,29,31,33] and appended terms a(35) and a(36), by running Meringer's GENREG for 17 and 106 processor days at U. Ncle, on May 04 2010.

a(37) appended from running GENREG for 450 processor days at U. Ncle. by Jason Kimberley, Dec 03 2011