Finite topologies

Brendan McKay bdm at
Tue Oct 9 17:38:06 CEST 2001

Sequence A001930 lists the number of isomorphism types of finite
topologies up to only 7 points:

%I A001930 M2817 N1133
%S A001930 1,1,3,9,33,139,718,4535
%N A001930 Topologies or transitive digraphs with n unlabeled nodes.
%D A001930 K. K.-H. Butler and G. Markowsky, Enumeration of finite topologies, Proc. 4th S-E Conf. Combin., Graph Theory, Computing, Congress. Numer. 8 (1973), 169-184.
%D A001930 F. Harary and E. M. Palmer, Graphical Enumeration, Academic Press, NY, 1973, p. 218 (but the last entry is wrong).
%D A001930 J. A. Wright, There are 718 6-point topologies, quasi-orderings, and transgraphs, Notices Amer. Math. Soc., 17 (1970), p. 646, Abstract #70T-A106.
%D A001930 J. A. Wright, personal communication.
%K A001930 nonn,hard,nice
%O A001930 0,3
%A A001930 njas

This is not very impressive in 2001, as a good program can get that
far in about 0.1 seconds.  So I'm wondering if there are any more
values out there.

Gunnar Brinkmann and I are computing them up to 16 points.


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