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A002218 Number of unlabeled nonseparable (or 2-connected) graphs (or blocks) with n nodes.
(Formerly M2873 N1155)
0, 1, 1, 3, 10, 56, 468, 7123, 194066, 9743542, 900969091, 153620333545, 48432939150704, 28361824488394169, 30995890806033380784, 63501635429109597504951, 244852079292073376010411280, 1783160594069429925952824734641, 24603887051350945867492816663958981 (list; graph; refs; listen; history; text; internal format)



By definition, a(n) counts the number of graphs with zero cutpoints. - Travis Hoppe, Apr 28 2014


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.

F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 188.

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.

R. W. Robinson and T. R. S. Walsh, Inversion of cycle index sum relations for 2- and 3-connected graphs. J. Combin. Theory Ser. B 57 (1993), no. 2, 289-308.

Andrew J. Schultz and David A. Kofke, Fifth to eleventh virial coefficients of hard spheres, Phys. Rev. E 90, 023301, 4 August 2014

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).


R. W. Robinson, Table of n, a(n) for n = 1..26

R. W. Robinson, Tables

R. W. Robinson and T. R. S. Walsh, Inversion of cycle index sum relations for 2- and 3-connected graphs, J. Combin. Theory Ser. B. 57 (1993), 289-308.

D. Stolee, Isomorph-free generation of 2-connected graphs with applications, arXiv preprint arXiv:1104.5261, 2011

Eric Weisstein's World of Mathematics, Biconnected Graph.

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


Cf. A000088, A001349, A006289, A006290, A004115, A013922, A241767.

Sequence in context: A081721 A013009 A203416 * A107871 A111270 A242953

Adjacent sequences:  A002215 A002216 A002217 * A002219 A002220 A002221




N. J. A. Sloane.


More terms from R. C. Read (rcread(AT)math.uwaterloo.ca). Robinson and Walsh list the first 26 terms.



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Last modified March 27 09:23 EDT 2015. Contains 255945 sequences.