A241706 -id:A241706 - cp's OEIS frontend

A294522 Triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with diameter k (0<=k

1, 0, 1, 0, 1, 1, 0, 1, 4, 1, 0, 1, 14, 5, 1, 0, 1, 59, 43, 8, 1, 0, 1, 373, 387, 82, 9, 1, 0, 1, 4154, 5797, 1027, 125, 12, 1, 0, 1, 91518, 148229, 19320, 1818, 180, 13, 1, 0, 1, 4116896, 6959721, 598913, 37856, 2928, 239, 16, 1

Offset: 1

Andrew Howroyd, Nov 01 2017

			Triangle begins:
  1;
  0, 1;
  0, 1,    1;
  0, 1,    4,    1;
  0, 1,   14,    5,    1;
  0, 1,   59,   43,    8,   1;
  0, 1,  373,  387,   82,   9,  1;
  0, 1, 4154, 5797, 1027, 125, 12, 1;
  ...
From _Eric W. Weisstein_, Jun 11 2019: (Start)
a(2,1) = 1 since only P_2 has diameter 1.
a(3,1) = 1 since only C_3 has diameter 1.
a(3,2) = 1 since only P_3 has diameter 2.
a(4,1) = 1 since only K_4 has diameter 1.
a(4,2) = 4 since K_1,3, K4-e, the paw graph, and C_4 have diameter 2.
a(4,3) = 1 since only P_4 has diameter 3.
(End)

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

Columns k=0..6 are A000007, A057427, A241706, A241707, A241708, A241709, A241710.

Row sums give A001349.

a(n,1) = 1 for n > 1 (only K_n has diameter 1).

a(n,n-1) = 1 (only P_n has diameter n-1).

A241707 Number of simple connected graphs on n nodes with diameter 3.

Original entry on oeis.org

0, 0, 0, 1, 5, 43, 387, 5797, 148229, 6959721

Offset: 1

Travis Hoppe and Anna Petrone, Apr 27 2014

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
Travis Hoppe and Anna Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
Peter Steinbach, Field Guide to Simple Graphs, Volume 1, Part 17 [But beware errors] (For Volumes 1, 2, 3, 4 of this book see A000088, A008406, A000055, A000664, respectively.)
Eric Weisstein's World of Mathematics, Graph Diameter

Column k=3 of A294522.

Simple connected graphs of diameter k: A241706, A241707, A241708, A241709, A241710.

A241708 Number of simple connected graphs on n nodes with diameter 4.

Original entry on oeis.org

0, 0, 0, 0, 1, 8, 82, 1027, 19320, 598913

Offset: 1

Travis Hoppe and Anna Petrone, Apr 27 2014

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
Travis Hoppe and Anna Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
Eric Weisstein's World of Mathematics, Graph Diameter

Column k=4 of A294522.

Cf. simple connected graph of diameter k A241706, A241707, A241708, A241709, A241710.

A241709 Number of simple connected graphs on n nodes with diameter 5.

Original entry on oeis.org

0, 0, 0, 0, 0, 1, 9, 125, 1818, 37856

Offset: 1

Travis Hoppe and Anna Petrone, Apr 27 2014

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
Travis Hoppe and Anna Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
Eric Weisstein's World of Mathematics, Graph Diameter

Column k=5 of A294522.

Cf. simple connected graph of diameter k A241706, A241707, A241708, A241709, A241710.

A241710 Number of simple connected graphs on n nodes with diameter 6.

Original entry on oeis.org

0, 0, 0, 0, 0, 0, 1, 12, 180, 2928

Offset: 1

Travis Hoppe and Anna Petrone, Apr 27 2014

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
Travis Hoppe and Anna Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644 [math.CO], 2014.
Eric Weisstein's World of Mathematics, Graph Diameter

Column k=6 of A294522.

Cf. simple connected graph of diameter k A241706, A241707, A241708, A241709, A241710.

A382283 Number of square roots of connected square graphs in the order listed in A382194.

Original entry on oeis.org

1, 1, 2, 1, 5, 1, 2, 3, 15, 1, 1, 2, 3, 4, 1, 3, 3, 15, 1, 1, 17, 60, 1, 2, 1, 2, 1, 1, 1, 1, 4, 2, 3, 2, 4, 11, 10, 11, 2, 1, 5, 3, 3, 6, 9, 8, 6, 1, 1, 19, 51, 3, 21, 1, 1, 3, 21, 2, 3, 113, 1, 11, 127, 374, 1, 1, 2, 3, 4, 1, 1, 2, 3, 4, 1, 1, 2, 1, 1, 1, 2

Offset: 1

Pontus von Brömssen, Mar 22 2025

A382194 lists all connected graphs that are squares, encoded as in A076184. a(n) is the number of unlabeled graphs whose squares are isomorphic to the n-th graph in A382194.

			As an irregular triangle, where row n >= 1 contains A382180(n) terms:
  1;
  1;
  2;
  1, 5;
  1, 2, 3, 15;
  1, 1, 2,  3, 4, 1, 3, 3, 15, 1, 1, 17, 60;
  ...
The last term on row n equals A241706(n)+1, the number of graphs whose square is the complete graph on n vertices.

Pontus von Brömssen, Table of n, a(n) for n = 1..1580 (for graphs on up to 9 vertices)
Eric Weisstein's World of Mathematics, Graph Square.
Wikipedia, Graph power.

Cf. A076184, A241706, A382180, A382194.

cp's OEIS Frontend

A294522 Triangle read by rows: T(n,k) is the number of simple connected graphs on n nodes with diameter k (0<=k

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A241707 Number of simple connected graphs on n nodes with diameter 3.

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A241708 Number of simple connected graphs on n nodes with diameter 4.

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A241709 Number of simple connected graphs on n nodes with diameter 5.

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A241710 Number of simple connected graphs on n nodes with diameter 6.

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A382283 Number of square roots of connected square graphs in the order listed in A382194.

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