

A002851


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


59



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

F. C. Bussemaker, S. Cobeljic, D. M. Cvetkovic, and J. J. Seidel, Cubic graphs on <= 14 vertices J. Combinatorial Theory Ser. B 23(1977), no. 23, 234235. MR0485524 (58 #5354).


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), A361407 (rooted connected cubic), A321305 (signed connected cubic), A000421 (connected cubic loopless multigraphs), A005967 (connected cubic multigraphs), A275744 (multisets).
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).


KEYWORD

nonn,nice


AUTHOR



EXTENSIONS

More terms from Ronald C. Read


STATUS

approved



