Search: id:A006820
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%I A006820 M1617
%S A006820 1,1,2,6,16,59,265,1544,10778,88168,805491,8037418,86221634,985870522,
%T A006820 11946487647,152808063181
%N A006820 Number of connected regular graphs of degree 4 (or quartic graphs) with 
               n nodes.
%D A006820 CRC Handbook of Combinatorial Designs, 1996, p. 648.
%D A006820 I. A. Faradzev, Constructive enumeration of combinatorial objects, pp. 
               131-135 of Probl\`{e}mes combinatoires et th\'{e}orie des graphes 
               (Orsay, 9-13 Juillet 1976). Colloq. Internat. du C.N.R.S., No. 260, 
               Centre Nat. Recherche Scient., Paris, 1978.
%D A006820 M. Meringer, Fast Generation of Regular Graphs and Construction of Cages. 
               Journal of Graph Theory, 30 (1999), 137-146. [From Jason Kimberley 
               (Jason.Kimberley(AT)newcastle.edu.au), Nov 24 2009]
%D A006820 R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
%D A006820 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A006820 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">
               Tables of Regular Graphs</a>
%H A006820 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               QuarticGraph.html">Link to a section of The World of Mathematics.</
               a>
%H A006820 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RegularGraph.html">Link to a section of The World of Mathematics.</
               a>
%Y A006820 Cf. A033301, A033483.
%Y A006820 Connected regular graphs of degree k: A002851 (k=3), A006820 (k=4), A006821 
               (k=5), A006822 (k=6), A014377 (k=7), A014378 (k=8), A014381 (k=9), 
               A014382 (k=10), A014384 (k=11).
%Y A006820 Sequence in context: A150029 A068787 A073959 this_sequence A131385 A027742 
               A033301
%Y A006820 Adjacent sequences: A006817 A006818 A006819 this_sequence A006821 A006822 
               A006823
%K A006820 nonn,nice,hard,more,new
%O A006820 5,3
%A A006820 N. J. A. Sloane (njas(AT)research.att.com).
%E A006820 Appended a(19) from running M. Meringer's GENREG for 79 hours. Jason 
               Kimberley (Jason.Kimberley(AT)newcastle.edu.au), Sep 04 2009
%E A006820 By running M. Meringer's GENREG for 44 processor days on ARCSgrid at 
               UNcle, a(20) was found by Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), 
               Nov 24 2009

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