Orthogonality graphs of matrices over commutative rings

Styrt Oleg Grigoryevich

Orthogonality graphs of matrices over commutative rings

Styrt O. G.

Styrt Oleg Grigoryevich

associate professor, MIPT, The Phystech School of Applied Mathematics and Computer Science, Chair of Discrete Mathematics

Published: 2023, vol. 27, issue 1, pp. 24–34

Download full text (In Russian)

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.

BibTeX

@article{IS-Styrt2023,
  author  = {Styrt, Oleg Grigoryevich},
  title   = {{Orthogonality graphs of matrices over commutative rings}},
  journal = {Intelligent Systems. Theory and Applications},
  year    = {2023},
  volume  = {27},
  number  = {1},
  pages   = {24--34},
}

AMSBIB

\Bibitem{IS-Styrt2023}
\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
\lang In Russian

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