Geodesic
Totally conjugate orthogonal quasigroups and complete graphs
Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 8, pp. 17-26

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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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     title = {Totally conjugate orthogonal quasigroups and complete graphs},
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G. B. Belyavskaya; T. V. Popovich. Totally conjugate orthogonal quasigroups and complete graphs. Fundamentalʹnaâ i prikladnaâ matematika, Tome 16 (2010) no. 8, pp. 17-26. http://geodesic.mathdoc.fr/item/FPM_2010_16_8_a1/