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 $\mathrm{M}_n(\mathbb{R})$ is equal to $4$ either if $n=3$ or $n>4$. 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 equal to $4$. 
Jose Maria Grau, Antonio Oller-Marcen, Carmen Tasis
math.RA