A243800 -id:A243800 - cp's OEIS frontend

A243801 Number of simple connected graphs on n nodes whose maximum size of an independent edge set is equal to 3.

0, 0, 0, 0, 0, 95, 830, 790, 1479, 2625

Offset: 1

Travis Hoppe and Anna Petrone, Jul 15 2014

An independent edge set is a subset of the edges such that no two edges in the subset share a vertex. A maximum independent edge set an independent edge set containing the largest possible number of edges among all independent edge sets.

The maximum size of an independent edge set is also called the matching number of the graph. - Andrew Howroyd, Sep 05 2019

Travis Hoppe and Anna Petrone, Encyclopedia of Finite Graphs
T. Hoppe and A. Petrone, Integer sequence discovery from small graphs, arXiv preprint arXiv:1408.3644, 2014
Eric Weisstein's World of Mathematics, Matching Number
Eric Weisstein's World of Mathematics, Maximum Independent Edge Set

Column k=2 of A325304.

Cf. A243800 (max size of independent edge set=2).

A325304 Irregular triangle read by rows: T(n,k) is the number of simple connected graphs on n unlabeled nodes with matching number k, (0 <= k <= floor(n/2)).

Original entry on oeis.org

1, 1, 0, 1, 0, 2, 0, 1, 5, 0, 1, 20, 0, 1, 16, 95, 0, 1, 22, 830, 0, 1, 29, 790, 10297, 0, 1, 37, 1479, 259563, 0, 1, 46, 2625, 166988, 11546911

Offset: 0

Andrew Howroyd, Sep 05 2019

			Triangle begins:
  1;
  1;
  0, 1;
  0, 2;
  0, 1,  5;
  0, 1, 20;
  0, 1, 16,   95;
  0, 1, 22,  830;
  0, 1, 29,  790,  10297;
  0, 1, 37, 1479, 259563;
  0, 1, 46, 2625, 166988, 11546911;
  ...

Eric Weisstein's World of Mathematics, Matching Number
Wikipedia, Matching (graph theory)

Columns k=2..3 are A243800, A243801.
Row sums are A001349.
Cf. A286951 (not necessarily connected).
Cf. A218463 (right diagonal, even terms).
Cf. A263341, A294490.

T(2*n, n) = A218463(n).

cp's OEIS Frontend

A243801 Number of simple connected graphs on n nodes whose maximum size of an independent edge set is equal to 3.

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