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

%I A007146 M2909 #45 Feb 16 2025 08:32:31
%S A007146 1,0,1,3,11,60,502,7403,197442,9804368,902818087,153721215608,
%T A007146 48443044675155,28363687700395422,30996524108446916915,
%U A007146 63502033750022111383196,244852545022627009655180986,1783161611023802810566806448531,24603891215865809635944516464394339
%N A007146 Number of unlabeled simple connected bridgeless graphs with n nodes.
%C A007146 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
%D A007146 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007146 Andrew Howroyd, <a href="/A007146/b007146.txt">Table of n, a(n) for n = 1..40</a> (terms 1..22 from R. J. Mathar)
%H A007146 P. Hanlon and R. W. Robinson, <a href="http://dx.doi.org/10.1016/0095-8956(82)90048-X">Counting bridgeless graphs</a>, J. Combin. Theory, B 33 (1982), 276-305, Table III.
%H A007146 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BridgelessGraph.html">Bridgeless Graph</a>
%H A007146 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>
%H A007146 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SimpleGraph.html">Simple Graph</a>
%H A007146 Gus Wiseman, <a href="/A007146/a007146.png">The a(3) = 1 through a(5) = 11 connected bridgeless graphs.</a>
%F A007146 a(n) = A001349(n) - A052446(n). - _Gus Wiseman_, Sep 02 2019
%o A007146 (PARI) \\ Translation of theorem 3.2 in Hanlon and Robinson reference. See A004115 for graphsSeries and A339645 for combinatorial species functions.
%o A007146 cycleIndexSeries(n)={my(gc=sLog(graphsSeries(n)), gcr=sPoint(gc)); sSolve( gc + gcr^2/2 - sRaise(gcr,2)/2, x*sv(1)*sExp(gcr) )}
%o A007146 NumUnlabeledObjsSeq(cycleIndexSeries(15)) \\ _Andrew Howroyd_, Dec 31 2020
%Y A007146 Cf. A005470 (number of simple graphs).
%Y A007146 Cf. A007145 (number of simple connected rooted bridgeless graphs).
%Y A007146 Cf. A052446 (number of simple connected bridged graphs).
%Y A007146 Cf. A263914 (number of simple bridgeless graphs).
%Y A007146 Cf. A263915 (number of simple bridged graphs).
%Y A007146 The labeled version is A095983.
%Y A007146 Row sums of A263296 if the first two columns are removed.
%Y A007146 BII-numbers of set-systems with spanning edge-connectivity >= 2 are A327109.
%Y A007146 Graphs with non-spanning edge-connectivity >= 2 are A327200.
%Y A007146 2-vertex-connected graphs are A013922.
%Y A007146 Cf. A000719, A001349, A002494, A261919, A327069, A327071, A327074, A327075, A327077, A327109, A327144, A327146.
%K A007146 nonn,nice
%O A007146 1,4
%A A007146 _N. J. A. Sloane_
%E A007146 Reference gives first 22 terms.