A007146
Number of unlabeled simple connected bridgeless graphs with n nodes.
Original entry on oeis.org
1, 0, 1, 3, 11, 60, 502, 7403, 197442, 9804368, 902818087, 153721215608, 48443044675155, 28363687700395422, 30996524108446916915, 63502033750022111383196, 244852545022627009655180986, 1783161611023802810566806448531, 24603891215865809635944516464394339
Offset: 1
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
- 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.
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).
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.
-
\\ 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
Reference gives first 22 terms.
A052446
Number of unlabeled simple connected bridged graphs on n nodes.
Original entry on oeis.org
0, 1, 1, 3, 10, 52, 351, 3714, 63638, 1912203, 103882478, 10338614868, 1892863194064, 639799762452639, 400857034314325045, 467526363203064793081, 1019286659457016864347582, 4170114225096278323394128049, 32130213534058019378134295287305
Offset: 1
- Jean-François Alcover, Table of n, a(n) for n = 1..22
- Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
- T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
- T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, Discr. Appl. Math. 201 (2016) 172-181
- Eric Weisstein's World of Mathematics, k-Edge-Connected Graph
- Eric Weisstein's World of Mathematics, Bridged Graph
- Eric Weisstein's World of Mathematics, Connected Graph
- Gus Wiseman, The a(2) = 1 through a(5) = 10 connected bridged graphs
Cf.
A001349 (number of simple connected graphs).
Cf.
A007146 (number of simple connected bridgeless graphs).
Cf.
A263914 (number of simple bridgeless graphs).
Cf.
A263915 (number of simple bridged graphs).
Row sums of
A327077 if the first column is removed.
BII-numbers of set-systems with spanning edge-connectivity 1 are
A327111.
-
A001349 = Cases[Import["https://oeis.org/A001349/b001349.txt", "Table"], {, }][[All, 2]];
A007146 = Cases[Import["https://oeis.org/A007146/b007146.txt", "Table"], {, }][[All, 2]] ;
a[n_] := A001349[[n + 1]] - A007146[[n]];
Array[a, 22] (* Jean-François Alcover, Nov 09 2019 *)
A263915
Number of (not necessarily connected) simple bridged graphs with n nodes.
Original entry on oeis.org
0, 1, 2, 6, 18, 79, 462, 4344, 69130, 1994511, 106159534, 10456891547, 1904341902688, 641869332391172, 401549418479234409, 467956969039256753054, 1019786043659665470506946, 4171198012616858743636651785, 32134630668466555232483869886654
Offset: 1
Cf.
A000088 (number of simple graphs).
Cf.
A007146 (number of simple connected bridgeless graphs).
Cf.
A052446 (number of simple connected bridged graphs).
Cf.
A263914 (number of simple bridgeless graph).
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