Search

Abstract Let R be a noncommutative ring with unity. The commuting graph of R , denoted by Γ (R) , is a graph whose vertices are noncentral elements of R and two distinct vertices x and y are adjacent if x y = y x. Let F be a finite field and n ≥ 2. It is conjectured by Akbari, Ghandehari, Hadian and Mohammadian in 2004 that if Γ (R) ≅ Γ (M n (F)) , then R ≅ M n (F). In this paper, we prove the conjecture whenever n is of the form 2 k 3 l with k ≠ 0. [ABSTRACT FROM AUTHOR]