On the diameter of the commuting graph of the matrix ring over a centrally finite division ring

摘要

For a finite dimensional division ring ID we establish a condition for the connectedness of the commuting graph Gamma(M-n(D)). Furthermore, if the graph Gamma(M-n(D)) is connected, we prove that its diameter cannot be greater that six. (C) 2016 Elsevier Inc. All rights reserved.