Title of article :
Non-Commuting Graphs and Some Bounds for Commutativity Degree of Finite Moufang Loops
Author/Authors :
Rezaie ، Elhameh Department of Mathematics - Islamic Azad University, Science and Research Branch , Ahmadidelir ، Karim Department of Mathematics - Islamic Azad University, Tabriz Branch , Tehranian ، Abolfazl Department of Mathematics - Islamic Azad University, Science and Research Branch , Rasouli ، Hamid Department of Mathematics - Islamic Azad University, Science and Research Branch
Abstract :
In this paper, we study some properties of the non-commuting graph ΓM 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.
Keywords :
Moufang loop , Chein loop , Non , commuting graph , Commutativity degree ,
Journal title :
Bulletin of the Iranian Mathematical Society
Journal title :
Bulletin of the Iranian Mathematical Society
