On non-commuting graph of a finite ring

2017/03/15 by J. Dutta, Dutta, J., D. K. Basnet +1
Mathematics · #05C25 #16U70 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:05C25 #msc:16U70

paper · pdf · doi:10.48550/arxiv.1703.05039

arxiv created 2017/03/15 · arxiv updated 2017/03/16

Abstract

The non-commuting graph Γ_R of a finite ring R with center Z(R) is a simple undirected graph whose vertex set is R ∖ Z(R) and two distinct vertices a and b are adjacent if and only if ab ≠ ba. In this paper, we show that Γ_R is not isomorphic to certain graphs of any finite non-commutative ring R. Some connections between Γ_R and commuting probability of R are also obtained. Further, it is shown that the non-commuting graphs of two ℤ-isoclinic rings are isomorphic if the centers of the rings have same order

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