A327074 Number of unlabeled connected graphs with n vertices and exactly one bridge.

0, 0, 1, 0, 1, 4, 25, 197, 2454, 48201, 1604016, 93315450, 9696046452, 1822564897453, 625839625866540, 395787709599238772, 464137745175250610865, 1015091996575508453655611, 4160447945769725861550193834, 32088553211819016484736085677320, 467409605282347770524641700949750858

Offset: 0

Author

Gus Wiseman, Aug 24 2019

Keywords

• nonn

Comments

A bridge is an edge that, if removed without removing any incident vertices, disconnects the graph. Unlabeled graphs with no bridges are counted by A007146 (unlabeled graphs with spanning edge-connectivity >= 2).

Links

• Gus Wiseman, The a(5) = 4 unlabeled connected graphs with n vertices and exactly one bridge.

Crossrefs

The labeled version is A327073.

Unlabeled graphs with at least one bridge are A052446.

The enumeration of unlabeled connected graphs by number of bridges is A327077.

BII-numbers of set-systems with spanning edge-connectivity >= 2 are A327109.

Cf. A001349, A002494, A007146, A263296, A327075, A327111, A327144, A327145.

Programs

Mathematica

A007145 = Cases[Import["https://oeis.org/A007145/b007145.txt", "Table"], {, }][[All, 2]];
f[x_] = A007145 . x^Range[lg = Length[A007145]];
(f[x]^2 + f[x^2])/2 + O[x]^lg // CoefficientList[#, x]& (* Jean-François Alcover, Sep 23 2019 *)

Formula

G.f.: (f(x)^2 + f(x^2))/2 where f(x) is the g.f. of A007145. - Andrew Howroyd, Aug 25 2019

Extensions

Terms a(6) and beyond from Andrew Howroyd, Aug 25 2019