|
%I M1656 #52 Sep 06 2023 01:12:19
%S 1,0,1,2,6,21,94,540,4207,42110,516344,7373924,118573592,2103205738,
%T 40634185402,847871397424,18987149095005,454032821688754,
%U 11544329612485981,310964453836198311,8845303172513781271
%N Number of unlabeled trivalent (or cubic) graphs with 2n nodes.
%C Because the triangle A051031 is symmetric, a(n) is also the number of (2n-4)-regular graphs on 2n vertices.
%D R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H G. Brinkmann, <a href="http://dx.doi.org/10.1002/(SICI)1097-0118(199610)23:2<139::AID-JGT5>3.0.CO;2-U">Fast generation of cubic graphs</a>, Journal of Graph Theory, 23(2):139-149, 1996.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/A051031">Not-necessarily connected regular graphs</a>
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/E_k-reg_girth_ge_g_index">Index of sequences counting not necessarily connected k-regular simple graphs with girth at least g</a>
%H R. W. Robinson, <a href="/A005636/a005636.pdf">Cubic graphs (notes)</a>
%H Robinson, R. W.; Wormald, N. C., <a href="http://dx.doi.org/10.1002/jgt.3190070412">Numbers of cubic graphs</a>, J. Graph Theory 7 (1983), no. 4, 463-467.
%H Peter Steinbach, <a href="/A000088/a000088_17.pdf">Field Guide to Simple Graphs, Volume 1</a>, Part 17 (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CubicGraph.html">Cubic Graph</a>
%H Gal Weitz, Lirandë Pira, Chris Ferrie, and Joshua Combes, <a href="https://arxiv.org/abs/2308.14981">Sub-universal variational circuits for combinatorial optimization problems</a>, arXiv:2308.14981 [quant-ph], 2023.
%F a(n) = A002851(n) + A165653(n).
%F This sequence is the Euler transformation of A002851.
%Y Cf. A000421.
%Y Row sums of A275744.
%Y 3-regular simple graphs: A002851 (connected), A165653 (disconnected), this sequence (not necessarily connected).
%Y Regular graphs A005176 (any degree), A051031 (triangular array), chosen degrees: A000012 (k=0), A059841 (k=1), A008483 (k=2), this sequence (k=3), A033301 (k=4), A165626 (k=5), A165627 (k=6), A165628 (k=7), A180260 (k=8).
%Y Not necessarily connected 3-regular simple graphs with girth *at least* g: this sequence (g=3), A185334 (g=4), A185335 (g=5), A185336 (g=6).
%Y Not necessarily connected 3-regular simple graphs with girth *exactly* g: A185133 (g=3), A185134 (g=4), A185135 (g=5), A185136 (g=6).
%K nonn,nice
%O 0,4
%A _N. J. A. Sloane_
%E More terms from Ronald C. Read.
%E Comment, formulas, and (most) crossrefs by _Jason Kimberley_, 2009 and 2012
|
