cp's OEIS Frontend

A010355 Number of unlabeled nonseparable (or 2-connected) graphs (or blocks) with n edges.

%I A010355 #38 Nov 06 2022 19:34:40
%S A010355 1,0,1,1,2,4,7,16,42,111,331,1094,3829,14380,57069,237188,1027929,
%T A010355 4622588,21494274,103077677,508743475,2579847563,13422868110,
%U A010355 71570635306,390670937143
%N A010355 Number of unlabeled nonseparable (or 2-connected) graphs (or blocks) with n edges.
%C A010355 Original name: Single-edge stars with n edges.
%H A010355 George A. Baker Jr. and John M. Kincaid, <a href="https://doi.org/10.1007/BF01012818">The continuous-spin Ising model, g0:phi4:d field theory and the renormalization group</a>. J. Statist. Phys. 24 (1981), no. 3, 469-528.
%H A010355 Brendan McKay and Adolfo Piperno, <a href="https://doi.org/10.1016/j.jsc.2013.09.003">Practical Graph Isomorphism, II</a>, Journal of Symbolic Computation, 60 (2014), pp. 94-112.
%H A010355 Brendan McKay and Adolfo Piperno, <a href="http://pallini.di.uniroma1.it/">nauty and Traces</a>, programs for computing automorphism groups of graphs and digraphs.
%H A010355 R. W. Robinson, <a href="http://web.archive.org/web/20041220072855/http://www.cs.uga.edu/~rwr/publications/tables.pdf">Tables of 2-Connected and 3-Connected Graphs by Nodes and Edges</a>, Table IV, pages 4-9.
%H A010355 M. F. Sykes, D. S. McKenzie, and B. R. Heap, <a href="https://doi.org/10.1088/0305-4470/7/13/012">Specific heat of a three-dimensional Ising ferromagnet above the Curie temperature. III. The star cluster expansion</a>, J. Phys. A: Math. Nucl. Gen., 7 (1974), 1576.
%e A010355 From _Andrew Howroyd_, Nov 23 2020: (Start)
%e A010355 The a(1) = 1 graph is the single edge (K_2 = P_2).
%e A010355 The a(3) = 1 graph is the triangle (K_3).
%e A010355 The a(4) = 1 graph is the square (C_4).
%e A010355 The a(5) = 2 graphs are the cycle C_5 and a cycle of 4 nodes with one diagonal added.
%e A010355 (End)
%Y A010355 Row sums of A339070 and A010356.
%Y A010355 Column sums of A339071.
%Y A010355 Cf. A002218, A010357, A322139, A338511.
%K A010355 nonn,more
%O A010355 1,5
%A A010355 _N. J. A. Sloane_
%E A010355 a(11)-a(12) from _Andrey Zabolotskiy_, Oct 03 2017
%E A010355 Name changed by _Andrew Howroyd_, Nov 23 2020
%E A010355 a(13)-a(18) added using data from Robinson's tables by _Andrew Howroyd_, Nov 23 2020
%E A010355 a(19)-a(22) from _Hugo Pfoertner_ using program geng from nauty, Dec 04 2020
%E A010355 a(23)-a(24) from _Hugo Pfoertner_, Dec 07 2020
%E A010355 a(25) from _Hugo Pfoertner_, Jan 04 2021