A001435 Number of connected graphs with n nodes and n+1 edges.

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

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

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. - Jonathan Vos Post, Jun 26 2010

References

• 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

• 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.

Crossrefs

Cf. A000055, A001429, A076263.

Extensions

Description corrected by and more terms from Ronald C. Read, Aug 02 1996

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