cp's OEIS Frontend

A014374 Number of trivalent connected simple graphs with 2n nodes and girth at least 6.

%I A014374 #34 Jul 08 2025 05:38:03
%S A014374 1,0,0,0,0,0,0,1,1,5,32,385,7574,181227,4624501,122090544,3328929954,
%T A014374 93990692595,2754222605376
%N A014374 Number of trivalent connected simple graphs with 2n nodes and girth at least 6.
%C A014374 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]
%D A014374 CRC Handbook of Combinatorial Designs, 1996, p. 647.
%D A014374 M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [_Jason Kimberley_, Jan 29 2011]
%H A014374 House of Graphs, <a href="https://houseofgraphs.org/meta-directory/cubic">Cubic graphs</a>
%H A014374 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_6">Connected regular graphs with girth at least 6</a>
%H A014374 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_k-reg_girth_ge_g_index">Index of sequences counting connected k-regular simple graphs with girth at least g</a>
%H A014374 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%H A014374 M. Meringer, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199902)30:2&lt;137::AID-JGT7&gt;3.0.CO;2-G">Fast generation of regular graphs and construction of cages</a>, J. Graph Theory 30 (2) (1999) 137-146. [_Jason Kimberley_, Jan 29 2011]
%Y A014374 From _Jason Kimberley_, May 18 2010 and Jan 29 2011: (Start)
%Y A014374 Connected k-regular simple graphs with girth at least 6: A186726 (any k), A186716 (triangle); specified degree k: A185116 (k=2), this sequence (k=3), A058348 (k=4).
%Y A014374 Connected 3-regular simple graphs with girth at least g: A185131 (triangle); chosen g: A002851 (g=3), A014371 (g=4), A014372 (g=5), this sequence (g=6), A014375 (g=7), A014376 (g=8).
%Y A014374 Connected 3-regular 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)
%K A014374 nonn,more,hard
%O A014374 0,10
%A A014374 _N. J. A. Sloane_
%E A014374 Terms a(16) and a(17) appended, from running Meringer's GENREG for 18.6 and 530 processor days at U. Ncle., by _Jason Kimberley_ on May 18 2010
%E A014374 Term a(18) from House of Graphs via _Jason Kimberley_, May 21 2017