Graphs defined by orthogonality.
Let \(R\) be an associative ring with identity. The vertex set of the orthogonal graph of the ring \(R\) consists of all nonzero two-sided zero-divisors of \(R\). Moreover, two vertices \(r_1,r_2\in R\) are connected by an edge iff \(r_1r_2=r_2r_1=0\), i.e. \(r_1\) and \(r_2\) are orthogonal. In this paper, properties of the orthogonal graphs of the full matrix algebra and other matrix sets are studied.
scientific article; zbMATH DE number 6537355
scientific article