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The commuting graph of a semigroup is the set of non-central elements; theedges are defined as pairs $(u,v)$ satisfying $uv=vu$. We provide an example ofa field $F$ and an integer $n$ such that the commuting graph of$\operatorname{Mat}_n(F)$ has maximal possible diameter, equal to six.

A matrix ring with commuting graph of maximal diameter