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A263296 Triangle read by rows: T(n,k) is the number of graphs with n vertices with edge connectivity k. 23

%I

%S 1,1,1,2,1,1,5,3,2,1,13,10,8,2,1,44,52,41,15,3,1,191,351,352,121,25,3,

%T 1,1229,3714,4820,2159,378,41,4,1,13588,63638,113256,68715,14306,1095,

%U 65,4,1,288597,1912203,4602039,3952378,1141575,104829,3441,100,5,1

%N Triangle read by rows: T(n,k) is the number of graphs with n vertices with edge connectivity k.

%C This is spanning edge-connectivity. The spanning edge-connectivity of a graph is the minimum number of edges that must be removed (without removing incident vertices) to obtain a graph that is disconnected or covers fewer vertices. The non-spanning edge-connectivity of a graph (A327236) is the minimum number of edges that must be removed to obtain a graph whose edge-set is disconnected or empty. Compare to vertex-connectivity (A259862). - _Gus Wiseman_, Sep 03 2019

%H FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000261">The edge connectivity of a graph</a>.

%H Jens M. Schmidt, <a href="/A324088/a324088.html">Combinatorial Data</a>

%H Gus Wiseman, <a href="/A263296/a263296.png">Unlabeled graphs with 5 vertices organized by spanning edge-connectivity (isolated vertices not shown).</a>

%e Triangle begins:

%e 1;

%e 1, 1;

%e 2, 1, 1;

%e 5, 3, 2, 1;

%e 13, 10, 8, 2, 1;

%e 44, 52, 41, 15, 3, 1;

%e 191, 351, 352, 121, 25, 3, 1;

%e 1229, 3714, 4820, 2159, 378, 41, 4, 1;

%e ...

%Y Row sums give A000088, n >= 1.

%Y Columns k=0..10 are A000719, A052446, A052447, A052448, A241703, A241704, A241705, A324096, A324097, A324098, A324099.

%Y Number of graphs with edge connectivity at least k for k=1..10 are A001349, A007146, A324226, A324227, A324228, A324229, A324230, A324231, A324232, A324233.

%Y The labeled version is A327069.

%Y Cf. A002494, A095983, A259862, A327076, A327108, A327109, A327111, A327144, A327145, A327147, A327236.

%K nonn,tabl

%O 1,4

%A _Christian Stump_, Oct 13 2015

%E a(22)-a(55) added by _Andrew Howroyd_, Aug 11 2019

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Last modified February 24 18:41 EST 2021. Contains 341577 sequences. (Running on oeis4.)