Authors: Krapež, Aleksandar 
Živković, Dejan
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Parastrophically equivalent quasigroup equations
Journal: Publications de l'Institut Mathematique
Volume: 87
Issue: 101
First page: 39
Last page: 58
Issue Date: 14-Oct-2010
Rank: M24
ISSN: 0350-1302
DOI: 10.2298/PIM1001039K
Fedir M. Sokhats'kyi recently posed four problems concerning parastrophic equivalence between generalized quasigroup functional equations. Sava Krstić in his PhD thesis established a connection between generalized quadratic quasigroup functional equations and connected cubic graphs. We use this connection to solve two of Sokhats'kyi's problems, giving also complete characterization of parastrophic cancellability of quadratic equations and reducing the problem of their classification to the problem of classification of connected cubic graphs. Further, we give formulas for the number of quadratic equations with a given number of variables. Finally, we solve all equations with two variables.
Keywords: Cubic graph | Parastrophic cancellability | Parastrophic equivalence | Quadratic functional equation | Quasigroup
Publisher: Mathematical Institute of the SASA
Project: Ministry of Science and Technology of Serbia, Grants 144013 and 144018

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