A324244 -id:A324244 - cp's OEIS frontend

A324239 Irregular triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with radius k, (0 <= k <= floor(n/2)).

1, 0, 1, 0, 2, 0, 4, 2, 0, 11, 10, 0, 34, 76, 2, 0, 156, 682, 15, 0, 1044, 9864, 207, 2, 0, 12346, 245518, 3197, 19, 0, 274668, 11366961, 74614, 326, 2

Offset: 1

Andrew Howroyd, Sep 02 2019

			Triangle begins:
  1;
  0,      1;
  0,      2;
  0,      4,        2;
  0,     11,       10;
  0,     34,       76,     2;
  0,    156,      682,    15;
  0,   1044,     9864,   207,   2;
  0,  12346,   245518,  3197,  19;
  0, 274668, 11366961, 74614, 326, 2;
  ...

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

Row sums give A001349.
Columns k=1..2 are A000088(n-1), A324061.
Cf. A283826, A294522, A294525, A324244.

A324263 Number of simple connected graphs on n unlabeled nodes with exactly two peripheral nodes.

Original entry on oeis.org

0, 1, 1, 2, 5, 25, 185, 2459, 58156, 2617378

Offset: 1

Andrew Howroyd, Sep 02 2019

These are the graphs that only have two nodes whose distance from each other is equal to the diameter. An example of such a graph is the path graph.

Column 2 of A324244.

A324264 Number of simple connected graphs on n unlabeled nodes with diameter equal to radius.

Original entry on oeis.org

1, 1, 1, 2, 5, 28, 223, 3151, 79673, 3853870

Offset: 1

Andrew Howroyd, Sep 02 2019

When the graph diameter is equal to the radius, every node has the same eccentricity and is in both the graph center and the graph periphery.

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

Rightmost diagonal of A294525 and A324244.

cp's OEIS Frontend

A324239 Irregular triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with radius k, (0 <= k <= floor(n/2)).

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A324263 Number of simple connected graphs on n unlabeled nodes with exactly two peripheral nodes.

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A324264 Number of simple connected graphs on n unlabeled nodes with diameter equal to radius.

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