A263296 - OEIS

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A263296

Triangle read by rows: T(n,k) is the number of graphs with n vertices with edge connectivity k.

1, 1, 1, 2, 1, 1, 5, 3, 2, 1, 13, 10, 8, 2, 1, 44, 52, 41, 15, 3, 1, 191, 351, 352, 121, 25, 3, 1, 1229, 3714, 4820, 2159, 378, 41, 4, 1, 13588, 63638, 113256, 68715, 14306, 1095, 65, 4, 1, 288597, 1912203, 4602039, 3952378, 1141575, 104829, 3441, 100, 5, 1

(list; table; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

This is spanning edge-connectivity. The spanning edge-connectivity of a graph is the minimum number of edges that must be removed (without removing incident vertices) to obtain a graph that is disconnected or covers fewer vertices. The non-spanning edge-connectivity of a graph (A327236) is the minimum number of edges that must be removed to obtain a graph whose edge-set is disconnected or empty. Compare to vertex-connectivity (A259862). - Gus Wiseman, Sep 03 2019

LINKS

Table of n, a(n) for n=1..55.

FindStat - Combinatorial Statistic Finder, The edge connectivity of a graph.

Jens M. Schmidt, Combinatorial Data

Gus Wiseman, Unlabeled graphs with 5 vertices organized by spanning edge-connectivity (isolated vertices not shown).

EXAMPLE

Triangle begins:

1, 1;

2, 1, 1;

5, 3, 2, 1;

13, 10, 8, 2, 1;

44, 52, 41, 15, 3, 1;