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

%I A263296 #32 Jan 08 2025 05:01:46
%S A263296 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 A263296 1,1229,3714,4820,2159,378,41,4,1,13588,63638,113256,68715,14306,1095,
%U A263296 65,4,1,288597,1912203,4602039,3952378,1141575,104829,3441,100,5,1
%N A263296 Triangle read by rows: T(n,k) is the number of graphs with n vertices with edge connectivity k.
%C A263296 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 A263296 Georg Grasegger, <a href="/A263296/b263296.txt">Table of n, a(n) for n = 1..78 (rows 1..12)</a>
%H A263296 FindStat - Combinatorial Statistic Finder, <a href="http://www.findstat.org/StatisticsDatabase/St000261">The edge connectivity of a graph</a>.
%H A263296 Jens M. Schmidt, <a href="/A324088/a324088.html">Combinatorial Data</a>
%H A263296 Gus Wiseman, <a href="/A263296/a263296.png">Unlabeled graphs with 5 vertices organized by spanning edge-connectivity (isolated vertices not shown).</a>
%e A263296 Triangle begins:
%e A263296      1;
%e A263296      1,    1;
%e A263296      2,    1,    1;
%e A263296      5,    3,    2,    1;
%e A263296     13,   10,    8,    2,   1;
%e A263296     44,   52,   41,   15,   3,  1;
%e A263296    191,  351,  352,  121,  25,  3, 1;
%e A263296   1229, 3714, 4820, 2159, 378, 41, 4, 1;
%e A263296   ...
%Y A263296 Row sums give A000088, n >= 1.
%Y A263296 Columns k=0..10 are A000719, A052446, A052447, A052448, A241703, A241704, A241705, A324096, A324097, A324098, A324099.
%Y A263296 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 A263296 The labeled version is A327069.
%Y A263296 Cf. A002494, A095983, A259862, A327076, A327108, A327109, A327111, A327144, A327145, A327147, A327236.
%K A263296 nonn,tabl
%O A263296 1,4
%A A263296 _Christian Stump_, Oct 13 2015
%E A263296 a(22)-a(55) added by _Andrew Howroyd_, Aug 11 2019