A014372 Number of trivalent connected simple graphs with 2n nodes and girth at least 5.

1, 0, 0, 0, 0, 1, 2, 9, 49, 455, 5783, 90938, 1620479, 31478584, 656783890, 14621871204, 345975648562

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• more
• hard

Comments

The null graph on 0 vertices is vacuously connected and 3-regular; since it is acyclic, it has infinite girth. - Jason Kimberley, Jan 29 2011

Brendan McKay has observed that a(13) = 31478584 is output by genreg, minibaum, and snarkhunter, but Meringer's table currently has a(13) = 31478582. - Jason Kimberley, May 17 2017

References

• CRC Handbook of Combinatorial Designs, 1996, p. 647.

Links

• G. Brinkmann, J. Goedgebeur and B. D. McKay, Generation of cubic graphs, Discr. Math. Theor. Comp. Sci. 13 (2) (2011) 69-80.
• House of Graphs, Cubic graphs.
• 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
• M. Meringer, Fast generation of regular graphs and construction of cages, J. Graph Theory 30 (2) (1999) 137-146.

Crossrefs

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

3-regular simple graphs with girth at least 5: this sequence (connected), A185235 (disconnected), A185335 (not necessarily connected).

Connected k-regular simple graphs with girth at least 5: A186725 (all k), A186715 (triangle); A185115 (k=2), this sequence (k=3), A058343 (k=4), A205295 (g=5).

Connected 3-regular simple graphs with girth at least g: A185131 (triangle); A002851 (g=3), A014371 (g=4), this sequence (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).

Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7). (End)

Extensions

Terms a(15) and a(16) appended, from running Meringer's GENREG for 28.7 and 715.2 processor days at U. Ncle., by Jason Kimberley, Jun 28 2010.