cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A181154 Number of connected 8-regular simple graphs on n vertices with girth at least 4.

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%I A181154 #27 Jan 19 2012 13:50:31
%S A181154 1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,1,0,13,1
%N A181154 Number of connected 8-regular simple graphs on n vertices with girth at least 4.
%C A181154 a(20) and a(21) were computed by the author, using GENREG, over 79 processor hours and 294 processor days, respectively, during Dec 2009.
%D A181154 M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. Journal of Graph Theory, 30 (1999), 137-146.
%H A181154 Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/C_girth_ge_4">Connected regular graphs with girth at least 4</a>
%H A181154 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 A181154 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">Tables of Regular Graphs</a>
%e A181154 The a( 0)=1 null graph is vacuously 8-regular and connected; since it is acyclic then it has infinite girth.
%e A181154 The a(16)=1 graph is the complete bipartite graph K_{8,8}.
%e A181154 The a(21)=1 graph has girth 4, automorphism group of order 829440, and the following adjacency lists:
%e A181154 01 : 02 03 04 05 06 07 08 09
%e A181154 02 : 01 10 11 12 13 14 15 16
%e A181154 03 : 01 10 11 12 13 14 15 16
%e A181154 04 : 01 10 11 12 13 14 15 16
%e A181154 05 : 01 10 11 12 13 14 15 16
%e A181154 06 : 01 10 11 12 17 18 19 20
%e A181154 07 : 01 10 11 13 17 18 19 20
%e A181154 08 : 01 10 12 13 17 18 19 20
%e A181154 09 : 01 11 12 13 17 18 19 20
%e A181154 10 : 02 03 04 05 06 07 08 21
%e A181154 11 : 02 03 04 05 06 07 09 21
%e A181154 12 : 02 03 04 05 06 08 09 21
%e A181154 13 : 02 03 04 05 07 08 09 21
%e A181154 14 : 02 03 04 05 17 18 19 20
%e A181154 15 : 02 03 04 05 17 18 19 20
%e A181154 16 : 02 03 04 05 17 18 19 20
%e A181154 17 : 06 07 08 09 14 15 16 21
%e A181154 18 : 06 07 08 09 14 15 16 21
%e A181154 19 : 06 07 08 09 14 15 16 21
%e A181154 20 : 06 07 08 09 14 15 16 21
%e A181154 21 : 10 11 12 13 17 18 19 20
%Y A181154 8-regular simple graphs with girth at least 4: this sequence (connected), A185284 (disconnected), A185384 (not necessarily connected).
%Y A181154 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), A058276 (k=6), A181153 (k=7), this sequence (k=8), A181170 (k=9).
%Y A181154 Connected 8-regular simple graphs with girth at least g: A184981 (triangle); chosen g: A014378 (g=3), this sequence (g=4).
%Y A181154 Connected 8-regular simple graphs with girth exactly g: A184980 (triangle); chosen g: A184983 (g=3).
%K A181154 nonn,more,hard
%O A181154 0,21
%A A181154 Jason Kimberley, week to Jan 31 2011