[Nauty-list] Nauty with Latin Squares

[damian]

Hello,

I am trying to recreate the cannonical construction method described in
article "Small Latin Square, Quasigroups and Loops" (as a Master Thesis -
we need the square with non trivial auto-isotopy group to prove a
hypothesis).

I experience some trouble when calling nauty to graph derived from
incomplete latin square with respect to a certain isotopism (in article
graph G2(L), where L may be unfinished square, consisting of k blocks+
extra edges are added to represent the sigma autotopism). Problem is, that
the call to nauty is too slow (0.1s to few seconds). I think I might be
doing some sort of fundamental mistake.

My program is in C++, but I have compiled nauty to a .a static library as C
program. I use sparse graph representation, where the graph is a digraph
(to correctly represent the cycles in autotopism sigma).

Thanks in advance for any advice or hint.
Damian Vizar
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