A325111 Triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with k articulation vertices, (0 <= k <= n).

1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 3, 2, 1, 0, 0, 10, 7, 3, 1, 0, 0, 56, 33, 17, 5, 1, 0, 0, 468, 244, 101, 32, 7, 1, 0, 0, 7123, 2792, 890, 242, 60, 9, 1, 0, 0, 194066, 52448, 11468, 2461, 527, 97, 12, 1, 0, 0, 9743542, 1690206, 239728, 35839, 6056, 1029, 155, 15, 1, 0, 0

Offset: 0

Author

Andrew Howroyd, Sep 05 2019

Keywords

• nonn
• tabl

Comments

Articulation vertices are also called cutpoints. These are vertices that when removed increase the component count of the graph.

Examples

			Triangle begins:
     1;
     1     0;
     1,    0,   0;
     1,    1,   0,   0;
     3,    2,   1,   0,  0;
    10,    7,   3,   1,  0, 0;
    56,   33,  17,   5,  1, 0, 0;
   468,  244, 101,  32,  7, 1, 0, 0;
  7123, 2792, 890, 242, 60, 9, 1, 0, 0;
  ...
		

Links

• Eric Weisstein's World of Mathematics, Articulation Vertex

Crossrefs

Columns k=0..5 are A002218(n>1), A241767, A241768, A241769, A241770, A241771.

Row sums are A001349.

Cf. A327077, A370064 (labeled version).

Extensions

Diagonal for k = n inserted by Andrew Howroyd, Feb 25 2024