A327077 Triangle read by rows where T(n,k) is the number of unlabeled simple connected graphs with n vertices and k bridges.

1, 1, 0, 0, 1, 0, 1, 0, 1, 0, 3, 1, 0, 2, 0, 11, 4, 3, 0, 3, 0, 60, 25, 14, 7, 0, 6, 0, 502, 197, 91, 34, 18, 0, 11, 0, 7403, 2454, 826, 267, 100, 44, 0, 23, 0, 197442, 48201, 11383, 2800, 831, 259, 117, 0, 47, 0

Offset: 0

Author

Gus Wiseman, Aug 26 2019

Keywords

• nonn
• more
• tabl

Comments

A bridge is an edge that, if removed without removing any incident vertices, disconnects the graph. Unlabeled connected graphs with no bridges are counted by A007146 (unlabeled graphs with spanning edge-connectivity >= 2).

Examples

			Triangle begins:
     1
     1    0
     0    1   0
     1    0   1   0
     3    1   0   2   0
    11    4   3   0   3  0
    60   25  14   7   0  6  0
   502  197  91  34  18  0 11  0
  7403 2454 826 267 100 44  0 23 0
  ...
		

Links

• Gus Wiseman, Unlabeled connected graphs with 5 vertices and k bridges.

Crossrefs

The labeled version is A327072.

Row sums are A001349.

Row sums without the k = 0 column are A052446.

Column k = 0 is A007146, if we assume A007146(0) = 1.

Column k = 1 is A327074.

Column k = n - 1 is A000055.

Cf. A002494, A327071, A327073, A327108, A327109, A327111, A327130, A327144, A327145, A327146.

Extensions

a(21)-a(54) from Andrew Howroyd, Aug 28 2019