hamidreza dorbidi

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 Rand two distinct vertices x and y are adjacent if xy=yx. Let Fbe a finite field and n ≥2. It is conjectured by Akbari, Ghandehari, Hadian and Mohammadian in 2004 that if Γ(R)\cong Γ(Mn(F)), then R\cong Mn(F). In this paper, we prove the conjecture whenever n is of the form 2^k3^l with k>0.