A369191 Number of labeled simple graphs covering n vertices with at most n edges.

1, 0, 1, 4, 34, 387, 5686, 102084, 2162168, 52693975, 1450876804, 44509105965, 1504709144203, 55563209785167, 2224667253972242, 95984473918245388, 4439157388017620554, 219067678811211857307, 11489425098298623161164, 638159082104453330569185

Offset: 0

Author

Gus Wiseman, Jan 17 2024

Keywords

• nonn

Comments

Row-sums of left portion of A054548.

Examples

			The a(0) = 1 through a(3) = 4 graphs:
  {}  .  {{1,2}}  {{1,2},{1,3}}
                  {{1,2},{2,3}}
                  {{1,3},{2,3}}
                  {{1,2},{1,3},{2,3}}
		

Crossrefs

The minimal case is A053530.

The connected case is A129271, unlabeled version A005703.

The case of equality is A367863, covering case of A367862.

This is the covering case of A369192, or A369193 for covered vertices.

The version for loop-graphs is A369194.

The unlabeled version is A370316.

A001187 counts connected graphs, unlabeled A001349.

A006125 counts graphs, unlabeled A000088.

A006129 counts covering graphs, unlabeled A002494.

A054548 counts graphs covering n vertices with k edges, with loops A369199.

A057500 counts connected graphs with n vertices and n edges.

A133686 counts choosable graphs, covering A367869.

A367867 counts non-choosable graphs, covering A367868.

Cf. A000169, A000272, A000666, A001429, A003465, A006649, A143543, A116508, A140638, A322661.

Programs

Mathematica

Table[Length[Select[Subsets[Subsets[Range[n], {2}]],Length[Union@@#]==n&&Length[#]<=n&]],{n,0,5}]

Formula

Inverse binomial transform of A369193.