FUNDAMENTALNAYA
I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

2010, VOLUME 16, NUMBER 8, PAGES 17-26

**Totally conjugate orthogonal quasigroups and complete graphs**

G. B. Belyavskaya

T. V. Popovich

Abstract

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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.

Location: http://mech.math.msu.su/~fpm/eng/k10/k108/k10802h.htm

Last modified: December 5, 2011