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

0,17

Comments

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

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

References

M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From Jason Kimberley, Dec 11 2009]

Links

Table of n, a(n) for n=0..22.

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

M. Meringer, Tables of Regular Graphs

Formula

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

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).

Sequence in context: A196002 A370151 A038296 * A184964 A185364 A085678

Adjacent sequences: A058273 A058274 A058275 * A058277 A058278 A058279

Keyword

nonn,more,hard

Author

N. J. A. Sloane, Dec 17 2000

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.

Status

approved