This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A327127 #18 Jan 07 2025 16:27:43 %S A327127 1,0,1,1,0,1,2,1,0,1,5,3,2,0,1,13,11,7,2,0,1 %N A327127 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 A327127 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 A327127 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 A327127 Brendan McKay, <a href="https://web.archive.org/web/20240229214130/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 A327127 Triangle begins: %e A327127 1 %e A327127 0 1 %e A327127 1 0 1 %e A327127 2 1 0 1 %e A327127 5 3 2 0 1 %e A327127 13 11 7 2 0 1 %Y A327127 Row sums are A000088. %Y A327127 Column k = 0 is A000719, if we assume A000719(0) = 1. %Y A327127 Column k = 1 is A052442, if we assume A052442(1) = 1 and A052442(2) = 0. %Y A327127 The labeled version is A327125. %Y A327127 A more standard version (zeros removed) is A259862. %Y A327127 Cf. A052443, A322389, A326786, A327082, A327098, A327100, A327113, A327126, A327128, A327197. %K A327127 nonn,more,tabl %O A327127 0,7 %A A327127 _Gus Wiseman_, Aug 25 2019