Geodesic
Near-totally conjugate orthogonal quasigroups
Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2014), pp. 89-96

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The near-totally conjugate orthogonal quasigroups (near-$totCO$-quasigroups), i.e., quasigroups for which there exist five (but there are no six) pairwise orthogonal conjugates, are studied. We consider six types of such quasigroups, connection between them and prove that for any integer $n\geq7$ which is relatively prime to 2,3 and 5 there exist near-$totCO$-quasigroups of order $n$ of any type. Three types of conjugate orthogonality graphs, associated with these quasigroups are characterized. 
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     author = {G. B. Belyavskaya and T. V. Popovich},
     title = {Near-totally conjugate orthogonal quasigroups},
     journal = {Buletinul Academiei de \c{S}tiin\c{t}e a Republicii Moldova. Matematica},
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G. B. Belyavskaya; T. V. Popovich. Near-totally conjugate orthogonal quasigroups. Buletinul Academiei de Ştiinţe a Republicii Moldova. Matematica, no. 3 (2014), pp. 89-96. http://geodesic.mathdoc.fr/item/BASM_2014_3_a8/