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A001349 Number of connected graphs with n nodes.
(Formerly M1657 N0649)
+0
28
1, 1, 1, 2, 6, 21, 112, 853, 11117, 261080, 11716571, 1006700565, 164059830476, 50335907869219, 29003487462848061, 31397381142761241960, 63969560113225176176277, 245871831682084026519528568, 1787331725248899088890200576580, 24636021429399867655322650759681644 (list; graph; listen)
OFFSET

0,4

COMMENT

Inverse Euler transform of A000088.

REFERENCES

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

P. Butler and R. W. Robinson, On the computer calculation of the number of nonseparable graphs, pp. 191 - 208 of Proc. Second Caribbean Conference Combinatorics and Computing (Bridgetown, 1977). Ed. R. C. Read and C. C. Cadogan. University of the West Indies, Cave Hill Campus, Barbados, 1977. vii+223 pp.

P. J. Cameron, Some sequences of integers, Discrete Math., 75 (1989), 89-102; also in "Graph Theory and Combinatorics 1988", ed. B. Bollobas, Annals of Discrete Math., 43 (1989), 89-102.

F. Harary, The number of linear, directed, rooted and connected graphs, Trans. Amer. Math. Soc., 78 (1955), 445-463.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, page 48, c(x). Also page 242.

M. Petkovsek and T. Pisanski, Counting disconnected structures: chemical trees, fullerenes, I-graphs and others, Croatica Chem. Acta, 78 (2005), 563-567.

R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.

R. W. Robinson, Enumeration of non-separable graphs, J. Combin. Theory 9 (1970), 327-356.

R. W. Robinson, Numerical implementation of graph counting algorithms, AGRC Grant, Math. Dept., Univ. Newcastle, Australia, 1978.

M. L. Stein and P. R. Stein, Enumeration of Linear Graphs and Connected Linear Graphs up to p = 18 Points. Report LA-3775, Los Alamos Scientific Laboratory of the University of California, Los Alamos, NM, Oct 1967.

Robin J. Wilson, Introduction to Graph Theory, Academic Press, 1972. (But see A126060!)

A. Milicevic and N. Trinajstic, "Combinatorial Enumeration in Chemistry", Chem. Modell., Vol. 4, (2006), pp. 405-469.

LINKS

N. J. A. Sloane, Table of n, a(n) for n = 0..75 [Computed using Keith Briggs's values for A000088]

P. J. Cameron, Sequences realized by oligomorphic permutation groups, J. Integ. Seqs. Vol. 3 (2000), #00.1.5.

E. Friedman, Illustration of small graphs

Gordon Royle, Small graphs

Eric Weisstein's World of Mathematics, Connected Graph.

Eric Weisstein's World of Mathematics, k-Connected Graph

Index entries for "core" sequences

CROSSREFS

Cf. A000088, A002218, A006290, A000719. Row sums of A054924.

Sequence in context: A076328 A128527 A128528 this_sequence A126060 A110306 A028936

Adjacent sequences: A001346 A001347 A001348 this_sequence A001350 A001351 A001352

KEYWORD

nonn,core,nice

AUTHOR

N. J. A. Sloane (njas(AT)research.att.com).

EXTENSIONS

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

Link fixed by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Oct 23 2009

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Last modified December 17 23:40 EST 2009. Contains 171025 sequences.


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