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Number of connected 6-regular simple graphs on n vertices with girth at least 4.
16

%I #29 May 01 2014 02:40:01

%S 1,0,0,0,0,0,0,0,0,0,0,0,1,0,1,1,9,6,267,3727,483012,69823723,

%T 14836130862

%N Number of connected 6-regular simple graphs on n vertices with girth at least 4.

%C The null graph on 0 vertices is vacuously connected and 6-regular; since it is acyclic, it has infinite girth. [From _Jason Kimberley_, Jan 30 2011]

%C Other than at n=0, this sequence first differs from A184964 at n = A054760(6,5) = 40.

%D M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146. [From _Jason Kimberley_, Dec 11 2009]

%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_4">Connected regular graphs with girth at least 4</a>

%H 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 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>

%F a(n) = A014377(n) - A184963(n).

%Y 6-regular simple graphs with girth at least 4: this sequence (connected), A185264 (disconnected), A185364 (not necessarily connected).

%Y Connected k-regular simple graphs with girth at least 4: A186724 (any k), A186714 (triangle); specified degree k: A185114 (k=2), A014371 (k=3), A033886 (k=4), A058275 (k=5), this sequence (k=6), A181153 (k=7), A181154 (k=8), A181170 (k=9).

%Y Connected 6-regular simple graphs with girth at least g: A006822 (g=3), this sequence (g=4).

%Y Connected 6-regular simple graphs with girth exactly g: A184963 (g=3), A184964 (g=4).

%K nonn,more,hard

%O 0,17

%A _N. J. A. Sloane_, Dec 17 2000

%E Terms a(19), a(20), and a(21), were appended, from running Meringer's GENREG at U. Ncle. for 51 processor days, by Jason Kimberley on Dec 11 2009.

%E a(22) was appended, from running Meringer's GENREG at U. Ncle. for 1620 processor days, by Jason Kimberley on Dec 10 2011.