

A052446


Number of unlabeled simple connected bridged graphs on n nodes.


25



0, 1, 1, 3, 10, 52, 351, 3714, 63638, 1912203, 103882478, 10338614868, 1892863194064, 639799762452639, 400857034314325045, 467526363203064793081, 1019286659457016864347582, 4170114225096278323394128049, 32130213534058019378134295287305
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OFFSET

1,4


COMMENTS

These are unlabeled connected graphs with spanning edgeconnectivity 1, where the spanning edgeconnectivity of a graph is the minimum number of edges that must be removed (without removing incident vertices) to obtain a disconnected or empty graph.  Gus Wiseman, Sep 02 2019


LINKS

JeanFrançois 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) 172181
Eric Weisstein's World of Mathematics, kEdgeConnected 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


FORMULA

a(n) = A001349(n)  A007146(n).


MATHEMATICA

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] (* JeanFrançois Alcover, Nov 09 2019 *)


CROSSREFS

Cf. other kedgeconnected unlabeled graph sequences A052446, A052447, A052448, A241703, A241704, A241705.
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).
Column k = 1 of A263296.
Row sums of A327077 if the first column is removed.
BIInumbers of setsystems with spanning edgeconnectivity 1 are A327111.
The labeled version is A327071.
Cf. A002494, A327069, A327074, A327109, A327144.
Sequence in context: A230740 A013201 A309885 * A290489 A002873 A309910
Adjacent sequences: A052443 A052444 A052445 * A052447 A052448 A052449


KEYWORD

nonn,hard


AUTHOR

Eric W. Weisstein, May 08 2000


EXTENSIONS

a(8) and a(9) and better description by Eric W. Weisstein, Nov 07 2010
a(10) from the Encyclopedia of Finite Graphs by Travis Hoppe and Anna Petrone, Apr 22 2014
Additional terms from A001349 and A007146 by Eric W. Weisstein, Oct 29 2015
a(18)a(22) from A001349 and A007146 by JeanFrançois Alcover, Nov 09 2019


STATUS

approved



