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

1, 1, 2, 3, 6, 14, 32, 90, 279, 942, 3468, 13777, 57747, 254671, 1170565, 5580706, 27487418, 139477796, 727458338, 3893078684, 21346838204, 119787629215, 687200870250

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• more

Comments

Original name: Multi-edge stars with n edges.

Examples

			From _Andrew Howroyd_, Nov 23 2020: (Start)
The a(1) = 1 graph is a single edge (K_2 = P_2).
The a(2) = 1 graph is a double edge.
The a(3) = 2 graphs are a triple edge and the triangle (K_3).
The a(4) = 3 graphs are a quadruple edge, a triangle with one double edge and the square (C_4).
(End)
		

Links

• George A. Baker Jr. and John M. Kincaid, The continuous-spin Ising model, g0:phi4:d field theory, and the renormalization group, J. Statist. Phys. 24 (1981), no. 3, 469-528.
• Brendan McKay and Adolfo Piperno, nauty and Traces, programs for computing automorphism groups of graphs and digraphs.
• Gus Wiseman, Non-isomorphic representatives of the a(1) = 1 through a(6) = 14 unlabeled 2-connected multigraphs.

Crossrefs

Row sums of A339160.

Cf. A050535, A076864, A010355, A010359.

A002218 counts unlabeled 2-connected graphs.

A013922 counts labeled 2-connected graphs.

A322140 is a labeled version.

Cf. A002905, A006444, A007718, A275307, A304887.

Extensions

Name changed by Andrew Howroyd, Dec 05 2020

a(11)-a(20) added using geng/multig from nauty by Andrew Howroyd, Dec 05 2020

a(21)-a(23) from Sean A. Irvine, Apr 18 2024