cp's OEIS Frontend

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

%I A058343 #31 May 01 2014 02:36:24
%S A058343 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,
%T A058343 132160608,4018022149,118369811960
%N A058343 Number of connected 4-regular simple graphs on n vertices with girth at least 5.
%C A058343 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]
%D A058343 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]
%H A058343 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_5">Connected regular graphs with girth at least 5</a>
%H A058343 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 A058343 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%Y A058343 Contribution from Jason Kimberley, 2010, 2011, and 2012: (Start)
%Y A058343 4-regular simple graphs with girth at least 5: this sequence (connected), A185245 (disconnected), A185345 (not necessarily connected).
%Y A058343 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).
%Y A058343 Connected 4-regular simple graphs with girth at least g: A006820 (g=3), A033886 (g=4), this sequence (g=5), A058348 (g=6).
%Y A058343 Connected 4-regular simple graphs with girth exactly g: A184943 (g=3), A184944 (g=4), A184945 (g=5). (End)
%K A058343 nonn,more,hard
%O A058343 0,21
%A A058343 _N. J. A. Sloane_, Dec 17 2000
%E A058343 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.