ON THE DIAMETER OF THE COMMUTING GRAPH OF THE FULL MATRIX RING OVER THE REAL NUMBERS

In a recent paper C. Miguel proved that the diameter of the commuting graph of the matrix ring Mn(R) is equal to 4 if either n = 3 or n ≥ 5. But the case n = 4 remained open, since the diameter could be 4 or 5. In this work we close the problem showing that also in this case the diameter is 4.