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

0,6

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

Table of n, a(n) for n=0..20.

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

Formula

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

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 *)

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.

Sequence in context: A065735 A212694 A182953 * A337167 A140094 A284859

Adjacent sequences: A327071 A327072 A327073 * A327075 A327076 A327077

Keyword

nonn

Author

Gus Wiseman, Aug 24 2019

Extensions

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

Status

approved