Graphs defined by orthogonality.

DOI10.1007/s10958-015-2393-6zbMath1343.16020OpenAlexW594740418MaRDI QIDQ906822

B. R. Bakhadly, Alexander E. Guterman, O. V. Markova

Publication date: 29 January 2016

Published in: Journal of Mathematical Sciences (New York) (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10958-015-2393-6

zbMATH Keywords

matrix ringscommuting graphscommutative ringszero divisor graphsassociative ringsorthogonal graphs of ringsorthogonality graphs

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Algebraic systems of matrices (15A30) Connectivity (05C40)

Related Items (12)

On automorphism group of orthogonality graph of finite semisimple rings ⋮ Orthogonality graphs of matrices over skew fields ⋮ Orthogonality for \((0, -1)\) tropical normal matrices ⋮ Orthograph related to mutual strong Birkhoff-James orthogonality in \(C^*\)-algebras ⋮ The automorphism group and fixing number of the orthogonality graph of the full matrix ring ⋮ Cayley-Dickson split-algebras: doubly alternative zero divisors and relation graphs ⋮ The orthogonality relation classifies finite-dimensional formally real simple Jordan algebras ⋮ Orthogonality graphs of direct sums of rings and semisimple Artinian rings ⋮ Automorphism group and fixing number of the orthogonality graph based on rank one upper triangular matrices ⋮ Relationship graphs of real Cayley-Dickson algebras ⋮ Orthomaps on formally real simple Jordan algebras ⋮ An alternative construction of graphs by associating with algorithmic approach on MV-algebras

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Commuting graphs of matrices over semirings.
• On the diameters of commuting graphs
• A further algebraic version of Cochran's theorem and matrix partial orderings
• Commuting graphs of full matrix rings over finite fields.
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• When a zero-divisor graph is planar or a complete \(r\)-partite graph
• Zero-divisor graphs, von Neumann regular rings, and Boolean algebras.
• On the zero-divisor graph of a commutative ring
• On commuting graphs of semisimple rings
• Extremal matrix centralizers
• Automorphisms of the poset of skew projections
• On zero-divisor graphs of finite rings.
• Zero-divisor graphs of non-commutative rings.
• Non-commuting graph of a group.
• Commuting graphs of some subsets in simple rings
• The diameter of a zero divisor graph
• Commuting graphs and extremal centralizers
• The diameters of commuting graphs of linear groups and matrix rings over the integers modulo m
• On maximal distances in a commuting graph
• On Operator Commutators
• Commutativity in Finite Matrices
• ON THE COMMUTING GRAPH ASSOCIATED WITH THE SYMMETRIC AND ALTERNATING GROUPS
• Commuting Graphs of Matrix Algebras
• On Commuting Graphs of Finite Matrix Rings

This page was built for publication: Graphs defined by orthogonality.