A007146 Number of unlabeled simple connected bridgeless graphs with n nodes.

1, 0, 1, 3, 11, 60, 502, 7403, 197442, 9804368, 902818087, 153721215608, 48443044675155, 28363687700395422, 30996524108446916915, 63502033750022111383196, 244852545022627009655180986, 1783161611023802810566806448531, 24603891215865809635944516464394339

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• nice

Comments

Also unlabeled simple graphs with spanning edge-connectivity >= 2. The spanning edge-connectivity of a set-system is the minimum number of edges that must be removed (without removing incident vertices) to obtain a set-system that is disconnected or covers fewer vertices. - Gus Wiseman, Sep 02 2019

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..40 (terms 1..22 from R. J. Mathar)
• P. Hanlon and R. W. Robinson, Counting bridgeless graphs, J. Combin. Theory, B 33 (1982), 276-305, Table III.
• Eric Weisstein's World of Mathematics, Bridgeless Graph
• Eric Weisstein's World of Mathematics, Connected Graph
• Eric Weisstein's World of Mathematics, Simple Graph
• Gus Wiseman, The a(3) = 1 through a(5) = 11 connected bridgeless graphs.

Crossrefs

Cf. A005470 (number of simple graphs).

Cf. A007145 (number of simple connected rooted bridgeless graphs).

Cf. A052446 (number of simple connected bridged graphs).

Cf. A263914 (number of simple bridgeless graphs).

Cf. A263915 (number of simple bridged graphs).

The labeled version is A095983.

Row sums of A263296 if the first two columns are removed.

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

Graphs with non-spanning edge-connectivity >= 2 are A327200.

2-vertex-connected graphs are A013922.

Cf. A000719, A001349, A002494, A261919, A327069, A327071, A327074, A327075, A327077, A327109, A327144, A327146.

Programs

PARI

\\ Translation of theorem 3.2 in Hanlon and Robinson reference. See A004115 for graphsSeries and A339645 for combinatorial species functions.
cycleIndexSeries(n)={my(gc=sLog(graphsSeries(n)), gcr=sPoint(gc)); sSolve( gc + gcr^2/2 - sRaise(gcr,2)/2, x*sv(1)*sExp(gcr) )}
NumUnlabeledObjsSeq(cycleIndexSeries(15)) \\ Andrew Howroyd, Dec 31 2020

Formula

a(n) = A001349(n) - A052446(n). - Gus Wiseman, Sep 02 2019

Extensions

Reference gives first 22 terms.