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A001435 Number of connected graphs with n nodes and n+1 edges.
(Formerly M3889 N1597)
0, 0, 0, 1, 5, 19, 67, 236, 797, 2678, 8833, 28908, 93569, 300748, 959374, 3042808, 9597679, 30134509, 94218306, 293509092, 911325798, 2821327949, 8711297753, 26833501800, 82476837698, 253007383067, 774737986836 (list; graph; refs; listen; history; text; internal format)



This enumerates the connected graphs of complexity 2, in the terminology of Spencer, p.720. We define the complexity of a component [of the random graph] with V vertices and E edges as E-V+1. Trees [A000055] and unicyclic graphs [A001429] have complexity 0 and 1, respectively, and are called simple. A diagonal of A076263. [From Jonathan Vos Post, Jun 26 2010]


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).


Sean A. Irvine, Table of n, a(n) for n = 1..40

Joel Spencer, The Giant Component: The Golden Anniversary, Notices of the AMS, Vol. 57, No. 6, June/July 2010, 720-724

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.


Cf. A000055, A001429, A076263. [Jonathan Vos Post, Jun 26 2010]

Sequence in context: A035344 A114277 A104496 * A092492 A070857 A143954

Adjacent sequences:  A001432 A001433 A001434 * A001436 A001437 A001438




N. J. A. Sloane.


Description corrected by and more terms from Ron Read (rcread(AT)math.uwaterloo.ca), Aug 02 1996

a(27) corrected by Sean A. Irvine, Jul 23 2012



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Last modified October 1 13:04 EDT 2020. Contains 337443 sequences. (Running on oeis4.)