Graphs with automorphism groups of given order

[Jens Voss]

Hello SeqFans,

Exactly one year ago I started a thread named "Automorphismengruppen von Graphen"
in the German newsgroup "de.sci.mathematik" in which I asked for the vertex number
of a minimal graph with automorphism group of order n.

The discussion brought some interesting estimations and resulted in a sequence
which I just submitted to the OEIS:

%S A000001 0, 2, 9, 4, 15, 3, 14, 4, 15, 5, 22, 5, 26, 7, 21, 6, 34, 9, 38,
           7, 23, 11, 46, 4, 30, 13, 24, 9, 58, 14, 62
%N A000001 The number of vertices of the minimal graph with automorphism
           group of order n
%C A000001 Most terms were found in the thread "Automorphismengruppen von
           Graphen" in the German newsgroup "de.sci.mathematik" (mostly by
           Hauke Klein).
           The terms a(9)=15, a(15)=21, a(21)=23, a(27)=24, a(30)=14 still
           need verification.
%e A000001 a(4)=4 because the graph with 4 vertices and exactly one edge has
           an automorphism group of order 4 and no smaller graph has exactly
           4 automorphisms.
%O A000001 1
%K A000001 ,more,nice,nonn,

Is somebody able to verify the terms mentioned in the comment? The numbers
given are upper bounds, and I believe they cannot be improved.

Regards,
Jens