Aleksandar Krapež – Generalized quadratic functional equations on ternary quasigroups
Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade, Serbia
Quadratic quasigroup functional equations were introduced in  as a
natural generalization of permutational (usually called balanced) functional equations
on quasigroups. A fairly wide class of quadratic equations were solved in the same paper.
General case for binary quasigroups was solved by S. Krstić in his PhD thesis
, using the correspondence between such equations and certain connected
multigraphs. A slightly different version of such graphs is named Krstić graphs in
We generalize Krstić's results proving the existence of analogous correspondence
between generalized quadratic functional equations on ternary quasigroups and
connected multigraphs of degree 4. This also generalizes some recent results by
F.M. Sokhatsky et all. , . We also pose some related problems.
Strictly quadratic functional equations on quasigroups I,
Publ. Math, Inst. (Beograd) 29 (43) (1981), 125–138,
A. Krapež, M.A. Taylor,
Gemini functional equations on quasigroups,
Publ. Math. Debrecen 47 (1995), 281–292.
Quadratic quasigroup identities (Serbian),
University of Belgrade (1985),
(acessed: Nov. 23, 2020).
F.M. Sokhatsky, H. Krainichuk, A. Tarasevich,
A classification of generalized functional equations on ternary quasigroups,
Bull. Donetsk Nat. Univ. Series A: Natural Sci. 1–2 (2017), 35–64.
F.M. Sokhatsky, A. Tarasevich,
Classification of generalized ternary quadratic quasigroup functional equations
of the length three,
Carpathian Math. Publ. 11(1) (2019), 179–192,