A058343 Number of connected 4-regular simple graphs on n vertices with girth at least 5.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 8, 131, 3917, 123859, 4131991, 132160608, 4018022149, 118369811960

Offset: 0

Author

N. J. A. Sloane, Dec 17 2000

Keywords

• nonn
• more
• hard

Comments

The null graph on 0 vertices is vacuously connected and 4-regular; since it is acyclic, it has infinite girth. [From Jason Kimberley, Jan 29 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 29 2011]

Links

• Jason Kimberley, Connected regular graphs with girth at least 5
• Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
• M. Meringer, Tables of Regular Graphs

Crossrefs

Contribution from Jason Kimberley, 2010, 2011, and 2012: (Start)

4-regular simple graphs with girth at least 5: this sequence (connected), A185245 (disconnected), A185345 (not necessarily connected).

Connected k-regular simple graphs with girth at least 5: A186725 (all k), A186715 (triangle); A185115 (k=2), A014372 (k=3), this sequence (k=4), A205295 (k=5).

Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), this sequence (g=5), A058348 (g=6).

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

Extensions

Terms a(27) and a(28) were appended by Jason Kimberley, from running Meringer's GENREG for 58 and 1563 processor days at U. Ncle, on Mar 19 and Jun 28 2010.