Abstract
In this paper, we study some properties of the non-commuting graph \(\varGamma _M\) of a finite Moufang loop M, a graph obtained by setting all non-central elements of M as the vertex set and defining two distinct vertices to be adjacent if and only if their commutator is non-identity. In particular, Hamiltonian as well as (weak) perfectness of non-commuting graphs of Chein loops are considered. We find several upper and lower bounds for commutativity degree of some classes of finite Moufang loops by means of edge number of their non-commuting graphs and algebraic properties.
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The authors gratefully appreciate the referees’ careful reading of the paper and useful comments.
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Communicated by Mohammad Shahryari.
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Rezaie, E., Ahmadidelir, K., Tehranian, A. et al. Non-Commuting Graphs and Some Bounds for Commutativity Degree of Finite Moufang Loops. Bull. Iran. Math. Soc. 47, 1849–1869 (2021). https://doi.org/10.1007/s41980-020-00476-5
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DOI: https://doi.org/10.1007/s41980-020-00476-5