A058275 Number of connected 5-regular simple graphs on 2n vertices with girth at least 4.

1, 0, 0, 0, 0, 1, 1, 7, 388, 406824, 1125022325, 3813549359274

Offset

0,8

Comments

The null graph on 0 vertices is vacuously connected and 5-regular; since it is acyclic, it has infinite girth. [From Jason Kimberley, Jan 30 2011]

References

M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From Jason Kimberley, Jan 30 2011]

Links

Table of n, a(n) for n=0..11.

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) = A185354(n) - A185254(n);

This sequence is the inverse Euler transformation of A185354. - Jason Kimberley, Nov 04 2011.

Crossrefs

Contribution from Jason Kimberley, Jan 30 and Nov 04 2011: (Start)

5-regular simple graphs on 2n vertices with girth at least 4: this sequence (connected), A185254 (disconnected), A185354 (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), this sequence (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).

Connected 5-regular simple graphs with girth at least g: A006821 (g=3), this sequence (g=4), A205295 (g=5).

Connected 5-regular simple graphs with girth exactly g: A184953 (g=3), A184954 (g=4), A184955 (g=5). (End)

Sequence in context: A374141 A112905 A293459 * A184954 A185354 A222893

Adjacent sequences: A058272 A058273 A058274 * A058276 A058277 A058278

Keyword

nonn,more,hard

Author

N. J. A. Sloane, Dec 17 2000

Extensions

Terms a(10) and a(11) appended, from running Meringer's GENREG for 3.8 and 7886 processor days at U. Ncle., by Jason Kimberley on Jun 28 2010.

Status

approved