A327077 - OEIS

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

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

OFFSET

0,11

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).

LINKS

Table of n, a(n) for n=0..54.

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

EXAMPLE

Triangle begins:

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