A052446 Number of unlabeled simple connected bridged graphs on n nodes.

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

Offset

1,4

Comments

These are unlabeled connected graphs with spanning edge-connectivity 1, where the spanning edge-connectivity 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

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

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] (* Jean-François Alcover, Nov 09 2019 *)

Crossrefs

Cf. other k-edge-connected 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.

BII-numbers of set-systems with spanning edge-connectivity 1 are A327111.

The labeled version is A327071.

Cf. A002494, A327069, A327074, A327109, A327144.

Sequence in context: A013201 A309885 A363209 * A362062 A373284 A290489

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 Jean-François Alcover, Nov 09 2019

Status

approved