A058276 Number of connected 6-regular simple graphs on n vertices with girth at least 4.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 9, 6, 267, 3727, 483012, 69823723, 14836130862

Offset: 0

Author

N. J. A. Sloane, Dec 17 2000

Keywords

• nonn
• more
• hard
• changed

Comments

The null graph on 0 vertices is vacuously connected and 6-regular; since it is acyclic, it has infinite girth. - Jason Kimberley, Jan 30 2011

Other than at n=0, this sequence first differs from A184964 at n = A054760(6,5) = 40.

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

6-regular simple graphs with girth at least 4: this sequence (connected), A185264 (disconnected), A185364 (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), A033886 (k=4), A058275 (k=5), this sequence (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).

Connected 6-regular simple graphs with girth at least g: A006822 (g=3), this sequence (g=4).

Connected 6-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4).

Formula

a(n) = A014377(n) - A184963(n).

Extensions

Terms a(19), a(20), and a(21), were appended, from running Meringer's GENREG at U. Ncle. for 51 processor days, by Jason Kimberley on Dec 11 2009

a(22) was appended, from running Meringer's GENREG at U. Ncle. for 1620 processor days, by Jason Kimberley on Dec 10 2011