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

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,    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;
  ...

Crossrefs

Row sums give A000088, n >= 1.

Columns k=0..10 are A000719, A052446, A052447, A052448, A241703, A241704, A241705, A324096, A324097, A324098, A324099.

Number of graphs with edge connectivity at least k for k=1..10 are A001349, A007146, A324226, A324227, A324228, A324229, A324230, A324231, A324232, A324233.

The labeled version is A327069.

Cf. A002494, A095983, A259862, A327076, A327108, A327109, A327111, A327144, A327145, A327147, A327236.

Sequence in context: A294758 A125800 A264698 * A259862 A182930 A372725

Adjacent sequences: A263293 A263294 A263295 * A263297 A263298 A263299

Keyword

nonn,tabl

Author

Christian Stump, Oct 13 2015

Extensions

a(22)-a(55) added by Andrew Howroyd, Aug 11 2019

Status

approved