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

Author

Eric W. Weisstein, May 08 2000

Keywords

• nonn
• hard

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

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.

Programs

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 *)

Formula

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

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