Complete graph decompositions and p-groupoids

zbMATH Open1435.20079arXiv1904.04856MaRDI QIDQ5219012

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Publication date: 6 March 2020

Abstract: We study P-groupoids that arise from certain decompositions of complete graphs. We show that left distributive P-groupoids are distributive, quasigroups. We characterize 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 such P-quasigroups have characteristic left and right multiplication groups, as well as the right multiplication group is isomorphic to the dihedral group.

Full work available at URL: https://arxiv.org/abs/1904.04856

zbMATH Keywords

complete graphsquandlesHamiltonian decompositionsP-groupoidsP-quasigroups

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Loops, quasigroups (20N05)

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