Search: id:A051031
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%I A051031
%S A051031 1,1,1,1,0,1,1,1,1,1,1,0,1,0,1,1,1,2,2,1,1,1,0,2,0,2,0,1,1,1,3,6,6,3,1,
%T A051031 1,1,0,4,0,16,0,4,0,1,1,1,5,21,60,60,21,5,1,1,1,0,6,0,266,0,266,0,6,0,
               1,
%U A051031 1,1,9,94,1547,7849,7849,1547,94,9,1,1,1,0,10,0,10786,0,367860,0,10786
%N A051031 Triangle of numbers of nonisomorphic regular graphs on n nodes and degrees 
               0 to n-1.
%C A051031 A graph in which every node has r edges is called an r-regular graph. 
               The triangle is symmetric because if an n-node graph is r-regular, 
               than its complement is (n - 1 - r)-regular and two graphs are isomorphic 
               if and only if their complements are isomorphic.
%D A051031 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), Sep 24 2009]
%H A051031 J. S. Kimberley, <a href="b051031.txt">Rows 1..16 of A051031 triangle, 
               flattened</a>. [From Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), 
               Sep 24 2009]
%H A051031 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               RegularGraph.html">Link to a section of The World of Mathematics.</
               a>
%H A051031 M. Meringer, <a href="http://www.mathe2.uni-bayreuth.de/markus/reggraphs.html">
               Tables of Regular Graphs</a>. [From Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), 
               Sep 24 2009]
%e A051031 a(8, 3) = 6. Edge-lists for the 6 3-regular 8-node graphs:
%e A051031 Graph 1: 12, 13, 14, 23, 24, 34, 56, 57, 58, 67, 68, 78
%e A051031 Graph 2: 12, 13, 14, 24, 34, 26, 37, 56, 57, 58, 68, 78
%e A051031 Graph 3: 12, 13, 23, 14, 47, 25, 58, 36, 45, 67, 68, 78
%e A051031 Graph 4: 12, 13, 23, 14, 25, 36, 47, 48, 57, 58, 67, 68
%e A051031 Graph 5: 12, 13, 24, 34, 15, 26, 37, 48, 56, 57, 68, 78
%e A051031 Graph 6: 12, 23, 34, 45, 56, 67, 78, 18, 15, 26, 37, 48.
%Y A051031 Row sums give A005176.
%Y A051031 Derived from the aforementioned symmetry and the following sequences 
               that count regular graphs of degree k: A008483 (k=2), A005638 (k=3), 
               A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7). [From 
               Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), Sep 24 2009]
%Y A051031 Sequence in context: A004562 A123550 A004578 this_sequence A111915 A066520 
               A088526
%Y A051031 Adjacent sequences: A051028 A051029 A051030 this_sequence A051032 A051033 
               A051034
%K A051031 nonn,tabl
%O A051031 1,18
%A A051031 Eric Weisstein (eric(AT)weisstein.com)
%E A051031 More terms and comments from David Wasserman (dwasserm(AT)earthlink.net), 
               Feb 22 2002
%E A051031 More terms from Eric Weisstein (eric(AT)weisstein), Oct 19, 2002
%E A051031 Description corrected (changed 'orders' to 'degrees') by Jason Kimberley 
               (Jason.Kimberley(AT)newcastle.edu.au), Sep 06 2009
%E A051031 Extended to the sixteenth row (in the b-file) by Jason Kimberley (Jason.Kimberley(AT)newcastle.edu.au), 
               Sep 24 2009

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