A275867 Number of simple disconnected asymmetric graph on n vertices.

0, 0, 0, 0, 0, 0, 8, 144, 3552, 131452, 7840396, 797524408

Offset: 1

Author

Eric W. Weisstein, May 19 2017

Keywords

• nonn

Comments

For 2 < n < 12, a(n) = A124059(n-1) (connected asymmetric graphs). This is because the singleton is the only asymmetric graph with fewer than 6 vertices, so in a disconnected asymmetric graph with fewer than 12 vertices one connected component must be the singleton, and it cannot occur more than once. - Falk Hüffner, Jan 16 2020

References

• 1

Links

• Eric Weisstein's World of Mathematics, Graph Automorphism
• Eric Weisstein's World of Mathematics, Identity Graph

Crossrefs

Cf. A003400 (not-necessarily connected simple asymmetric graphs).

Cf. A124059 (connected simple asymmetric graphs).

Programs

Mathematica

A[s_Integer] := With[{s6 = StringPadLeft[ToString[s], 6, "0"]}, Cases[ Import[ "https://oeis.org/A" <> s6 <> "/b" <> s6 <> ".txt", "Table"], {, }][[All, 2]]];
A003400 = A@003400;
A124059 = A@124059;
a[n_] := A003400[[n]] - A124059[[n]];
a /@ Range[12] (* Jean-François Alcover, Jan 07 2020 *)

Formula

a(n) = A003400(n) - A124059(n).

Extensions

a(12) from Jean-François Alcover, Jan 07 2020