cp's OEIS Frontend

A033886 Number of connected 4-regular simple graphs on n vertices with girth at least 4.

%I A033886 #37 Sep 02 2025 09:22:28
%S A033886 1,0,0,0,0,0,0,0,1,0,2,2,12,31,220,1606,16828,193900,2452818,32670330,
%T A033886 456028474,6636066099,100135577747,1582718912968
%N A033886 Number of connected 4-regular simple graphs on n vertices with girth at least 4.
%C A033886 The null graph on 0 vertices is vacuously connected and 4-regular; since it is acyclic, it has infinite girth. - _Jason Kimberley_, Jan 29 2011
%H A033886 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_4">Connected regular graphs with girth at least 4</a>.
%H A033886 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 A033886 Markus Meringer, <a href="https://doi.org/10.1002/(SICI)1097-0118(199902)30:2%3C137::AID-JGT7%3E3.0.CO;2-G">Fast Generation of Regular Graphs and Construction of Cages</a>, Journal of Graph Theory, Vol. 30, No. 2 (1999), 137-146.
%H A033886 Markus Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>.
%Y A033886 From _Jason Kimberley_, Mar 19 2010 and Jan 28 2011: (Start)
%Y A033886 4-regular simple graphs with girth at least 4: this sequence (connected), A185244 (disconnected), A185344 (not necessarily connected).
%Y A033886 Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), this sequence (k=4), A058275 (k=5), A058276 (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).
%Y A033886 Connected 4-regular simple graphs with girth at least g: A006820 (g=3), this sequence (g=4), A058343 (g=5), A058348 (g=6).
%Y A033886 Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)
%K A033886 nonn,nice,more,hard,changed
%O A033886 0,11
%A A033886 _N. J. A. Sloane_, Dec 17 2000
%E A033886 By running M. Meringer's GENREG at U. Newcastle for 6.25, 107 and 1548 processor days, a(21), a(22), and a(23) were completed by _Jason Kimberley_ on Dec 06 2009, Mar 19 2010, and Nov 02 2011.