Geodesic
Distances on the Commuting Graph of the Ring of Real Martices
Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 765-768

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The vertices of the commuting graph of a semigroup $S$ are the noncentral elements of this semigroup, and its edges join all pairs of elements $g$, $h$ that satisfy the relation $gh=hg$. The paper presents a proof of the fact that the diameter of the commuting graph of the semigroup of real matrices of order $n\ge 3$ is equal to 4. A survey of results in that subject matter is presented, and several open problems are formulated.
Keywords: commuting graph, matrix theory. 
@article{MZM_2018_103_5_a10,
     author = {Ya. Shitov},
     title = {Distances on the {Commuting} {Graph} of the {Ring} of {Real} {Martices}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {765--768},
     publisher = {mathdoc},
     volume = {103},
     number = {5},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a10/}
}
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Ya. Shitov. Distances on the Commuting Graph of the Ring of Real Martices. Matematičeskie zametki, Tome 103 (2018) no. 5, pp. 765-768. http://geodesic.mathdoc.fr/item/MZM_2018_103_5_a10/