Complete graph decompositions and P-groupoids
© 2019, Institute of Mathematics, Academy of Sciences Moldova. All rights reserved. We study P-groupoids that arise from certain decompositions of complete graphs. We show that left distributive P-groupoids are distributive, quasigroups. We characterize some P-groupoids when the corresponding decomposition is a Hamiltonian decomposition for complete graphs of odd, prime order. We also study a specific example of a P-quasigroup constructed from cyclic groups of odd order. We show that the right multiplication group of such P-quasigroups is isomorphic to the dihedral group.
Quasigroups and Related Systems
Carr, J., & Greer, M. (2019). Complete graph decompositions and P-groupoids. Quasigroups and Related Systems. Retrieved from https://ir.una.edu/math_facpub/4