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arXiv · 2208.03039

Orthogonality graphs of matrices over commutative rings

O. G. Styrt
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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.

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O. G. Styrt. 2022-08-05. Orthogonality graphs of matrices over commutative rings. https://arxiv.org/abs/2208.03039

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