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%I #15 Jan 02 2023 12:30:54
%S 1,0,1,1,0,1,2,1,0,1,5,3,2,0,1,13,11,7,2,0,1
%N Triangle read by rows where T(n,k) is the number of unlabeled simple graphs with n vertices where k is the minimum number of vertices that must be removed (along with any incident edges) to obtain a disconnected or empty graph.
%C A graph with one vertex and no edges is considered to be connected. Except for complete graphs, this is the same as vertex-connectivity (A259862).
%C There are two ways to define (vertex) connectivity: the minimum size of a vertex cut, and the minimum of the maximum number of internally disjoint paths between two distinct vertices. For non-complete graphs they coincide, which is tremendously useful. For complete graphs with at least 2 vertices, there are no cuts but the second method still works so it is customary to use it to justify the connectivity of K_n being n-1. - _Brendan McKay_, Aug 28 2019.
%H Brendan McKay, <a href="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.
%e Triangle begins:
%e 1
%e 0 1
%e 1 0 1
%e 2 1 0 1
%e 5 3 2 0 1
%e 13 11 7 2 0 1
%Y Row sums are A000088.
%Y Column k = 0 is A000719, if we assume A000719(0) = 1.
%Y Column k = 1 is A052442, if we assume A052442(1) = 1 and A052442(2) = 0.
%Y The labeled version is A327125.
%Y A more standard version (zeros removed) is A259862.
%Y Cf. A052443, A322389, A326786, A327082, A327098, A327100, A327113, A327126, A327128, A327197.
%K nonn,more,tabl
%O 0,7
%A _Gus Wiseman_, Aug 25 2019
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