cp's OEIS Frontend

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.

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.

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%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