Graphs defined by orthogonality.
type: Item
instance of: scholarly article
title: Graphs defined by orthogonality.
zbMATH Open document ID: 1343.16020
author: B. R. Bakhadly
author: Alexander Guterman
author: O. V. Markova
published in: Journal of Mathematical Sciences (New York)
publication date: 2016-01-29T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 16S50
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C40
Mathematics Subject Classification ID: 05C50
Mathematics Subject Classification ID: 15A30
zbMATH DE Number: 6537355
zbMATH Keywords: associative rings
zbMATH Keywords: commutative rings
zbMATH Keywords: matrix rings
zbMATH Keywords: orthogonal graphs of rings
zbMATH Keywords: zero divisor graphs
zbMATH Keywords: commuting graphs
zbMATH Keywords: orthogonality graphs
MaRDI profile type: Publication
full work available at URL: s10958-015-2393-6
OpenAlex ID: W594740418
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DOI: 10.1007/S10958-015-2393-6
description: scientific article; zbMATH DE number 6537355