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A327127
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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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9
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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)
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OFFSET
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0,7
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COMMENTS
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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.
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LINKS
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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.
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EXAMPLE
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Triangle begins:
1
0 1
1 0 1
2 1 0 1
5 3 2 0 1
13 11 7 2 0 1
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CROSSREFS
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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
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KEYWORD
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nonn,more,tabl
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AUTHOR
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Gus Wiseman, Aug 25 2019
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STATUS
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approved
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