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A002851
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Number of unlabeled trivalent (or cubic) connected graphs with 2n nodes.
(Formerly M1521 N0595)
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51
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1, 0, 1, 2, 5, 19, 85, 509, 4060, 41301, 510489, 7319447, 117940535, 2094480864, 40497138011, 845480228069, 18941522184590, 453090162062723, 11523392072541432, 310467244165539782, 8832736318937756165
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,4
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REFERENCES
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CRC Handbook of Combinatorial Designs, 1996, p. 647.
F. Harary, Graph Theory. Addison-Wesley, Reading, MA, 1969, p. 195.
R. C. Read, Some applications of computers in graph theory, in L. W. Beineke and R. J. Wilson, editors, Selected Topics in Graph Theory, Academic Press, NY, 1978, pp. 417-444.
R. C. Read and G. F. Royle, Chromatic roots of families of graphs, pp. 1009-1029 of Y. Alavi et al., eds., Graph Theory, Combinatorics and Applications. Wiley, NY, 2 vols., 1991.
R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence)
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LINKS
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Table of n, a(n) for n=0..20.
G. Brinkmann, J. Goedgebeur and B. D. McKay, Generation of cubic graphs, Discr. Math. Theor. Comp. Sci. 13 (2) (2011) 69-80
G. Brinkmann, J. Goedgebeur, N. Van Cleemput, The history of the generation of cubic graphs, Int. J. Chem. Modeling 5 (2-3) (2013) 67-89
F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, Computer investigations of cubic graphs, T.H.-Report 76-WSK-01, Technological University Eindhoven, Dept. Mathematics, 1976.
F. C. Bussemaker, S. Cobeljic, D. M. Cvetkovic, J. J. Seidel, Cubic graphs on <= 14 vertices J. Combinatorial Theory Ser. B 23(1977), no. 2-3, 234--235. MR0485524 (58 #5354).
Timothy B. P. Clark, Adrian Del Maestro, Moments of the inverse participation ratio for the Laplacian on finite regular graphs, arXiv:1506.02048 [math-ph], 2015.
H. Gropp, Enumeration of regular graphs 100 years ago, Discrete Math., 101 (1992), 73-85.
House of Graphs, Cubic graphs
Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g
M. Klin, M. Rücker, Ch. Rücker and G. Tinhofer, Algebraic Combinatorics [broken link]
M. Klin, M. Rücker, Ch. Rücker, G. Tinhofer, Algebraic Combinatorics (1997)
Denis S. Krotov, Konstantin V. Vorob'ev, On unbalanced Boolean functions attaining the bound 2n/3-1 on the correlation immunity, arXiv:1812.02166 [math.CO], 2018.
R. J. Mathar/Wikipedia, Table of simple cubic graphs [From N. J. A. Sloane, Feb 28 2012]
M. Meringer, Tables of Regular Graphs
R. W. Robinson and N. C. Wormald, Numbers of cubic graphs. J. Graph Theory 7 (1983), no. 4, 463-467.
Sage, Common Graphs (Graph Generators)
J. J. Seidel, R. R. Korfhage, & N. J. A. Sloane, Correspondence 1975
H. M. Sultan, Separating pants decompositions in the pants complex.
H. M. Sultan, Net of Pants Decompositions Containing a non-trivial Separating Curve in the Pants Complex, arXiv:1106.1472 [math.GT], 2011.
Eric Weisstein's World of Mathematics, Connected Graph
Eric Weisstein's World of Mathematics, Cubic Graph
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EXAMPLE
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G.f. = 1 + x^2 + 2*x^3 + 5*x^4 + 19*x^5 + 85*x^6 + 509*x^7 + 4060*x^8 + 41302*x^9 + 510489*x^10 + 7319447*x^11 + ...
a(0) = 1 because the null graph (with no vertices) is vacuously 3-regular.
a(1) = 0 because there are no simple connected cubic graphs with 2 nodes.
a(2) = 1 because the tetrahedron is the only cubic graph with 4 nodes.
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CROSSREFS
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Cf. A004109 (labeled connected cubic), A321304 (rooted connected cubic), A321305 (signed connected cubic), A000421 (connected cubic multigraphs).
Contribution (almost all) from Jason Kimberley, Feb 10 2011: (Start)
3-regular simple graphs: this sequence (connected), A165653 (disconnected), A005638 (not necessarily connected), A005964 (planar).
Connected regular graphs A005177 (any degree), A068934 (triangular array), specified degree k: this sequence (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).
Connected 3-regular simple graphs with girth at least g: A185131 (triangle); chosen g: this sequence (g=3), A014371 (g=4), A014372 (g=5), A014374 (g=6), A014375 (g=7), A014376 (g=8).
Connected 3-regular simple graphs with girth exactly g: A198303 (triangle); chosen g: A006923 (g=3), A006924 (g=4), A006925 (g=5), A006926 (g=6), A006927 (g=7). (End)
Sequence in context: A286886 A058132 A286071 * A324618 A316700 A124348
Adjacent sequences: A002848 A002849 A002850 * A002852 A002853 A002854
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KEYWORD
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nonn,nice
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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More terms from R. C. Read (rcread(AT)math.uwaterloo.ca)
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STATUS
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approved
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