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A259862 Triangle read by rows: T(n,k) = number of unlabeled graphs with n nodes and connectivity exactly k (n>=1, 0<=k<=n-1).

%I A259862 #43 Jan 07 2025 11:11:11
%S A259862 1,1,1,2,1,1,5,3,2,1,13,11,7,2,1,44,56,39,13,3,1,191,385,332,111,21,3,
%T A259862 1,1229,3994,4735,2004,345,34,4,1,13588,67014,113176,66410,13429,992,
%U A259862 54,4,1,288597,1973029,4629463,3902344,1109105,99419,3124,81,5,1,12297299,105731474,327695586,388624106,162318088,21500415,820956,9813,121,5,1
%N A259862 Triangle read by rows: T(n,k) = number of unlabeled graphs with n nodes and connectivity exactly k (n>=1, 0<=k<=n-1).
%C A259862 These are vertex-connectivities. Spanning edge-connectivity is A263296. Non-spanning edge-connectivity is A327236. Cut-connectivity is A327127. - _Gus Wiseman_, Sep 03 2019
%H A259862 Georg Grasegger, <a href="/A259862/b259862.txt">Table of n, a(n) for n = 1..78</a>
%H A259862 Brendan McKay, <a href="https://web.archive.org/web/*/http://list.seqfan.eu/oldermail/seqfan/2015-July/015022.html">confusion over k-connected graphs</a>, posting to Sequence Fans Mailing List, Jul 08 2015.
%H A259862 Jens M. Schmidt, <a href="/A324088/a324088.html">Combinatorial Data</a>
%H A259862 Gus Wiseman, <a href="/A259862/a259862.png">The graphs counted by row n = 5 (isolated vertices not shown).</a>
%e A259862 Triangle begins:
%e A259862        1;
%e A259862        1,       1;
%e A259862        2,       1,       1;
%e A259862        5,       3,       2,       1;
%e A259862       13,      11,       7,       2,       1;
%e A259862       44,      56,      39,      13,       3,     1;
%e A259862      191,     385,     332,     111,      21,     3,    1;
%e A259862     1229,    3994,    4735,    2004,     345,    34,    4,  1;
%e A259862    13588,   67014,  113176,   66410,   13429,   992,   54,  4, 1;
%e A259862   288597, 1973029, 4629463, 3902344, 1109105, 99419, 3124, 81, 5, 1;
%e A259862   12297299,105731474,327695586,388624106,162318088,21500415,820956,9813,121,5,1;
%e A259862   ...
%Y A259862 Columns k=0..10 (up to initial nonzero terms) are A000719, A052442, A052443, A052444, A052445, A324234, A324235, A324088, A324089, A324090, A324091.
%Y A259862 Row sums are A000088.
%Y A259862 Number of graphs with connectivity at least k for k=1..10 are A001349, A002218, A006290, A086216, A086217, A324240, A324092, A324093, A324094, A324095.
%Y A259862 The labeled version is A327334.
%Y A259862 Cf. A002494, A263296, A322389, A326786, A327127, A327236.
%K A259862 nonn,tabl
%O A259862 1,4
%A A259862 _N. J. A. Sloane_, Jul 08 2015