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A002851 Number of unlabeled trivalent (or cubic) connected graphs with 2n nodes.
(Formerly M1521 N0595)
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)



Bussemaker, F. C.; Čobeljić, S.; Cvetković, D. M.; Seidel, J. J.Cubic graphs on <= 14 vertices. J. Combinatorial Theory Ser. B 23(1977), no. 2-3, 234--235. MR0485524 (58 #5354)

CRC Handbook of Combinatorial Designs, 1996, p. 647.

H. Gropp, Enumeration of regular graphs 100 years ago, Discrete Math., 101 (1992), 73-85.

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.

R. W. Robinson and N. C. Wormald, Numbers of cubic graphs. J. Graph Theory 7 (1983), no. 4, 463-467.

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)

H. Sultan, Separating pants decompositions in the pants complex, http://www.math.columbia.edu/~hsultan/papers/separatingpantscomplex_v3.pdf.


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

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 [From N. J. A. Sloane, Jan 12 2012].

House of Graphs, Cubic graphs

Jason Kimberley, Index of sequences counting connected k-regular simple graphs with girth at least g

M. Klin, M. R\"ucker, Ch. R\"ucker and G. Tinhofer, Algebraic Combinatorics [broken link]

M. Klin, M. Rucker, Ch. Rucker, G. Tinhofer, Algebraic Combinatorics (1997)

R. J. Mathar/Wikipedia, Table of simple cubic graphs [From N. J. A. Sloane, Feb 28 2012]

M. Meringer, Tables of Regular Graphs

Sage, Common Graphs (Graph Generators)

H. M. Sultan, Net of Pants Decompositions Containing a non-trivial Separating Curve in the Pants Complex, arXiv:1106.1472, 2011

Eric Weisstein's World of Mathematics, Cubic Graph


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.


Contribution (almost all) from Jason Kimberley, Feb 10 2011: (Start)

3-regular simple graphs: this sequence (connected), A165653 (disconnected), A005638 (not necessarily connected).

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: A179566 A107377 A058132 * A124348 A205804 A052324

Adjacent sequences:  A002848 A002849 A002850 * A002852 A002853 A002854




N. J. A. Sloane.


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



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Last modified April 23 14:18 EDT 2014. Contains 240931 sequences.