A052446 - OEIS

%I #54 Nov 10 2019 01:40:08

%S 0,1,1,3,10,52,351,3714,63638,1912203,103882478,10338614868,

%T 1892863194064,639799762452639,400857034314325045,

%U 467526363203064793081,1019286659457016864347582,4170114225096278323394128049,32130213534058019378134295287305

%N Number of unlabeled simple connected bridged graphs on n nodes.

%C 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

%H Jean-François Alcover, <a href="/A052446/b052446.txt">Table of n, a(n) for n = 1..22</a>

%H Travis Hoppe and Anna Petrone, <a href="https://github.com/thoppe/Encyclopedia-of-Finite-Graphs">Encyclopedia of Finite Graphs</a>

%H T. Hoppe and A. Petrone, <a href="http://arxiv.org/abs/1408.3644">Integer sequence discovery from small graphs</a>, arXiv preprint arXiv:1408.3644 [math.CO], 2014.

%H T. Hoppe and A. Petrone, <a href="http://doi.org/10.1016/j.dam.2015.07.017">Integer sequence discovery from small graphs</a>, Discr. Appl. Math. 201 (2016) 172-181

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/k-Edge-ConnectedGraph.html">k-Edge-Connected Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BridgedGraph.html">Bridged Graph</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConnectedGraph.html">Connected Graph</a>

%H Gus Wiseman, <a href="/A052446/a052446.png">The a(2) = 1 through a(5) = 10 connected bridged graphs</a>

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

%t A001349 = Cases[Import["https://oeis.org/A001349/b001349.txt", "Table"], {_, _}][[All, 2]];

%t A007146 = Cases[Import["https://oeis.org/A007146/b007146.txt", "Table"], {_, _}][[All, 2]] ;

%t a[n_] := A001349[[n + 1]] - A007146[[n]];

%t Array[a, 22] (* _Jean-François Alcover_, Nov 09 2019 *)

%Y Cf. other k-edge-connected unlabeled graph sequences A052446, A052447, A052448, A241703, A241704, A241705.

%Y Cf. A001349 (number of simple connected graphs).

%Y Cf. A007146 (number of simple connected bridgeless graphs).

%Y Cf. A263914 (number of simple bridgeless graphs).

%Y Cf. A263915 (number of simple bridged graphs).

%Y Column k = 1 of A263296.

%Y Row sums of A327077 if the first column is removed.

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

%Y The labeled version is A327071.

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

%K nonn,hard

%O 1,4

%A _Eric W. Weisstein_, May 08 2000

%E a(8) and a(9) and better description by _Eric W. Weisstein_, Nov 07 2010

%E a(10) from the Encyclopedia of Finite Graphs by _Travis Hoppe_ and _Anna Petrone_, Apr 22 2014

%E Additional terms from A001349 and A007146 by _Eric W. Weisstein_, Oct 29 2015

%E a(18)-a(22) from A001349 and A007146 by _Jean-François Alcover_, Nov 09 2019