O. G. Styrt, “Orthogonality graphs of matrices over commutative rings”, Intelligent systems. Theory and applications, 27:1 (2023), 24

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Intelligent systems. Theory and applications, 2023, Volume 27, Issue 1, Pages 24–34 (Mi ista498)

Part 2. Special Issues in Intellectual Systems Theory

Orthogonality graphs of matrices over commutative rings

O. G. Styrt

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract: The paper is devoted to studying the orthogonality graph of the matrix ring over a commutative ring. It is proved that the orthogonality graph of the ring of matrices with size greater than 1 over a commutative ring with zero-divisors is connected and has diameter 3 or 4; a criterion for each value is obtained. It is also shown that each of its vertices has distance at most 2 from some scalar matrix.

Keywords: associative ring with identity, commutative ring, zero-divisor, matrix ring, zero-divisor graph, orthogonality graph.

Document Type: Article

Language: Russian

Citation: O. G. Styrt, “Orthogonality graphs of matrices over commutative rings”, Intelligent systems. Theory and applications, 27:1 (2023), 24–34

Citation in format AMSBIB

\Bibitem{Sty23}

\by O.~G.~Styrt

\paper Orthogonality graphs of matrices over commutative rings

\jour Intelligent systems. Theory and applications

\yr 2023

\vol 27

\issue 1

\pages 24--34

\mathnet{http://mi.mathnet.ru/ista498}

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https://www.mathnet.ru/eng/ista498

https://www.mathnet.ru/eng/ista/v27/i1/p24

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