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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. 9
1, 0, 1, 1, 0, 1, 2, 1, 0, 1, 5, 3, 2, 0, 1, 13, 11, 7, 2, 0, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,7

COMMENTS

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).

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.

LINKS

Table of n, a(n) for n=0..20.

Brendan McKay, confusion over k-connected graphs, posting to Sequence Fans Mailing List, Jul 08 2015.

EXAMPLE

Triangle begins:

   1

   0  1

   1  0  1

   2  1  0  1

   5  3  2  0  1

  13 11  7  2  0  1

CROSSREFS

Row sums are A000088.

Column k = 0 is A000719, if we assume A000719(0) = 1.

Column k = 1 is A052442, if we assume A052442(1) = 1 and A052442(2) = 0.

The labeled version is A327125.

A more standard version (zeros removed) is A259862.

Cf. A052443, A322389, A326786, A327082, A327098, A327100, A327113, A327126, A327128, A327197.

Sequence in context: A351641 A291883 A239145 * A151824 A275514 A180782

Adjacent sequences:  A327124 A327125 A327126 * A327128 A327129 A327130

KEYWORD

nonn,more,tabl

AUTHOR

Gus Wiseman, Aug 25 2019

STATUS

approved

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Last modified July 6 10:13 EDT 2022. Contains 355109 sequences. (Running on oeis4.)