A324693 Number of simple graphs on n unlabeled nodes with minimum degree exactly 1.

0, 1, 1, 4, 12, 60, 378, 3843, 64455, 1921532, 104098702, 10348794144, 1893781768084, 639954768875644, 400905675004630820, 467554784370658979194, 1019317687720204607541914, 4170177760438554428852944352, 32130458453030025927403299167172

Offset: 1

Author

Andrew Howroyd, Sep 03 2019

Keywords

• nonn

Links

• Andrew Howroyd, Table of n, a(n) for n = 1..50
• Eric Weisstein's World of Mathematics, Minimum Vertex Degree
• Gus Wiseman, The a(2) = 1 through a(5) = 12 unlabeled graphs with minimum degree 1.

Crossrefs

Column k = 1 of A294217.

A diagonal of A263293.

The labeled version is A327227.

The generalization to set-systems is A327335, with covering case A327230.

Unlabeled covering graphs are A002494.

Cf. A000088, A004110, A100743, A141580, A245797, A261919, A327105, A327362, A327364, A327366, A327372.

Formula

a(n) = A002494(n) - A261919(n).

First differences of A141580. - Andrew Howroyd, Jan 11 2021