A324244 Triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with k peripheral nodes.

1, 0, 1, 0, 1, 1, 0, 2, 2, 2, 0, 5, 4, 7, 5, 0, 25, 20, 16, 23, 28, 0, 185, 146, 119, 57, 123, 223, 0, 2459, 1728, 1523, 948, 405, 903, 3151, 0, 58156, 36109, 32119, 24637, 13927, 4713, 11746, 79673, 0, 2617378, 1446609, 1304109, 1026845, 723871, 353620, 110734, 279535, 3853870

Offset: 1

Author

Andrew Howroyd, Sep 02 2019

Keywords

• nonn
• tabl

Comments

The peripheral nodes of a graph are those with eccentricity equal to the diameter.

Examples

			Triangle begins:
  1;
  0,     1;
  0,     1,     1;
  0,     2,     2,     2;
  0,     5,     4,     7,     5;
  0,    25,    20,    16,    23,    28;
  0,   185,   146,   119,    57,   123,  223;
  0,  2459,  1728,  1523,   948,   405,  903,  3151;
  0, 58156, 36109, 32119, 24637, 13927, 4713, 11746, 79673;
  ...
		

Links

• Eric Weisstein's World of Mathematics, Graph Periphery
• Wikipedia, Distance (graph theory)

Crossrefs

Row sums give A001349.

Column k=2 is A324263.

Rightmost diagonal is A324264.

Cf. A294522, A294525, A324239.