hamidreza dorbidi

The commuting graph of a non-commutative ring R denoted by 􀀀(R) is a graph whose vertices are non-central elements of R and two distinct vertices x and y are adjacent if xy = yx. Let D be a division ring, F = Z(D) and m2 = dimFD. In this paper, we show that if F ̸= D or n > 2 and the eld F has no extension of degree mn then 􀀀(Mn(D)) is a connected graph whose diameter is less than ve. Also we prove that the diameter of 􀀀(M2(H)) is four where H is a quaternion algebra over a eld F which has no extension of degree 4 and Char(F) ̸= 2.