Email this article Distances on the Commuting Graph of the Ring of Real Martices
- Authors: Shitov Y.N.1
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Affiliations:
- “Mathematical Notes,” Steklov Mathematical Institute of Russian Academy of Sciences
- Issue: Vol 103, No 5-6 (2018)
- Pages: 832-835
- Section: Article
- URL: https://journals.rcsi.science/0001-4346/article/view/150909
- DOI: https://doi.org/10.1134/S0001434618050152
- ID: 150909
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Abstract
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 ≥ 3 is equal to 4. A survey of results in that subject matter is presented, and several open problems are formulated.
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About the authors
Ya. N. Shitov
“Mathematical Notes,” Steklov Mathematical Institute of Russian Academy of Sciences
Author for correspondence.
Email: yaroslav-shitov@yandex.ru
Russian Federation, Moscow
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