

A002851


Number of unlabeled trivalent (or cubic) connected graphs with 2n nodes.
(Formerly M1521 N0595)


52



1, 0, 1, 2, 5, 19, 85, 509, 4060, 41301, 510489, 7319447, 117940535, 2094480864, 40497138011, 845480228069, 18941522184590, 453090162062723, 11523392072541432, 310467244165539782, 8832736318937756165
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OFFSET

0,4


REFERENCES

CRC Handbook of Combinatorial Designs, 1996, p. 647.
F. Harary, Graph Theory. AddisonWesley, 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. 417444.
R. C. Read and G. F. Royle, Chromatic roots of families of graphs, pp. 10091029 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)


LINKS

Table of n, a(n) for n=0..20.
Peter Adams, Ryan C. Bunge, Roger B. Eggleton, Saad I. ElZanati, Uğur Odabaşi, and Wannasiri Wannasit, Decompositions of complete graphs and complete bipartite graphs into bipartite cubic graphs of order at most 12, Bull. Inst. Combinatorics and Applications (2021) Vol. 92, 5061.
G. Brinkmann, J. Goedgebeur and B. D. McKay, Generation of cubic graphs, Discr. Math. Theor. Comp. Sci. 13 (2) (2011) 6980
G. Brinkmann, J. Goedgebeur, N. Van Cleemput, The history of the generation of cubic graphs, Int. J. Chem. Modeling 5 (23) (2013) 6789
F. C. Bussemaker, S. Cobeljic, L. M. Cvetkovic and J. J. Seidel, Computer investigations of cubic graphs, T.H.Report 76WSK01, 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. 23, 234235. 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 [mathph], 2015.
H. Gropp, Enumeration of regular graphs 100 years ago, Discrete Math., 101 (1992), 7385.
House of Graphs, Cubic graphs
Jason Kimberley, Index of sequences counting connected kregular 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/31 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, 463467.
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 nontrivial 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


EXAMPLE

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 3regular.
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.


CROSSREFS

Cf. A004109 (labeled connected cubic), A321304 (rooted connected cubic), A321305 (signed connected cubic), A000421 (connected cubic multigraphs), A275744 (multisets).
Contribution (almost all) from Jason Kimberley, Feb 10 2011: (Start)
3regular 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 3regular 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 3regular 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 A326563 A316700
Adjacent sequences: A002848 A002849 A002850 * A002852 A002853 A002854


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

More terms from R. C. Read (rcread(AT)math.uwaterloo.ca)


STATUS

approved



