A014375 Number of trivalent connected simple graphs with 2n nodes and girth at least 7.

1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 21, 546, 30368, 1782840, 95079083, 4686063120, 220323447962, 10090653722861

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn

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]

References

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

Links

• Jason Kimberley, Connected regular graphs with girth at least 7
• 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. [_Jason Kimberley_, May 29 2010]

Crossrefs

From Jason Kimberley, May 29 2010 and Jan 29 2011: (Start)

Connected k-regular simple graphs with girth at least 7: A186727 (any k), A186717 (triangle); specific k: A185117 (k=2), this sequence (k=3).

Trivalent simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), this sequence (g=7), A014376 (g=8).

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

Formula

a(n) = A006927(n) + A014376(n).

Extensions

Terms a(17), a(18), and a(19) found by running Meringer's GENREG for 1.9 hours, 99.6 hours, and 207.8 processor days, at U. Ncle., by Jason Kimberley, May 29 2010

Terms a(20) and a(21) from House of Graphs via Jason Kimberley, May 21 2017