

A007146


Number of unlabeled simple connected bridgeless graphs with n nodes.
(Formerly M2909)


29



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

1,4


COMMENTS

Also unlabeled simple graphs with spanning edgeconnectivity >= 2. The spanning edgeconnectivity of a setsystem is the minimum number of edges that must be removed (without removing incident vertices) to obtain a setsystem 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), 276305, 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.


FORMULA

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


PROG

(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


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.
BIInumbers of setsystems with spanning edgeconnectivity >= 2 are A327109.
Graphs with nonspanning edgeconnectivity >= 2 are A327200.
2vertexconnected graphs are A013922.
Cf. A000719, A001349, A002494, A261919, A327069, A327071, A327074, A327075, A327077, A327109, A327144, A327146.
Sequence in context: A136440 A303871 A231344 * A076475 A125556 A127516
Adjacent sequences: A007143 A007144 A007145 * A007147 A007148 A007149


KEYWORD

nonn,nice


AUTHOR

N. J. A. Sloane


EXTENSIONS

Reference gives first 22 terms.


STATUS

approved



