Abstract:
In this article, we study the spectrum of quasigroups all conjugates of which are distinct and pairwise orthogonal. We call such quasigroups totally conjugate orthogonal quasigroups (for brevity, totCO-quasigroups). Every totCO-quasigroup defines the complete conjugate orthogonal Latin square graph $K_6$. Examples of totCO-quasigroups of different orders are given.
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