cp's OEIS Frontend

A010357 Number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges.

%I A010357 #27 May 30 2024 19:13:04
%S A010357 1,1,2,3,6,14,32,90,279,942,3468,13777,57747,254671,1170565,5580706,
%T A010357 27487418,139477796,727458338,3893078684,21346838204,119787629215,
%U A010357 687200870250
%N A010357 Number of unlabeled nonseparable (or 2-connected) loopless multigraphs with n edges.
%C A010357 Original name: Multi-edge stars with n edges.
%H A010357 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 A010357 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 A010357 Gus Wiseman, <a href="/A010357/a010357.png">Non-isomorphic representatives of the a(1) = 1 through a(6) = 14 unlabeled 2-connected multigraphs</a>.
%e A010357 From _Andrew Howroyd_, Nov 23 2020: (Start)
%e A010357 The a(1) = 1 graph is a single edge (K_2 = P_2).
%e A010357 The a(2) = 1 graph is a double edge.
%e A010357 The a(3) = 2 graphs are a triple edge and the triangle (K_3).
%e A010357 The a(4) = 3 graphs are a quadruple edge, a triangle with one double edge and the square (C_4).
%e A010357 (End)
%Y A010357 Row sums of A339160.
%Y A010357 Cf. A050535, A076864, A010355, A010359.
%Y A010357 A002218 counts unlabeled 2-connected graphs.
%Y A010357 A013922 counts labeled 2-connected graphs.
%Y A010357 A322140 is a labeled version.
%Y A010357 Cf. A002905, A006444, A007718, A275307, A304887.
%K A010357 nonn,more
%O A010357 1,3
%A A010357 _N. J. A. Sloane_
%E A010357 Name changed by _Andrew Howroyd_, Dec 05 2020
%E A010357 a(11)-a(20) added using geng/multig from nauty by _Andrew Howroyd_, Dec 05 2020
%E A010357 a(21)-a(23) from _Sean A. Irvine_, Apr 18 2024