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

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

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 5-regular; since it is acyclic, it has infinite girth. - 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. - Jason Kimberley, Jan 30 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
• M. Meringer, Tables of Regular Graphs

Crossrefs

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)

Formula

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

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

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