A note on automorphisms of the zero-divisor graph of upper triangular matrices.

DOI10.1016/j.laa.2014.09.035zbMath1312.16026OpenAlexW2022183817MaRDI QIDQ471936

Long Wang

Publication date: 17 November 2014

Published in: Linear Algebra and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.laa.2014.09.035

zbMATH Keywords

directed graphszero-divisor graphsgraph automorphisms

Mathematics Subject Classification ID

Endomorphism rings; matrix rings (16S50) Automorphisms and endomorphisms (16W20) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25)

Related Items (27)

Automorphisms of the zero-divisor graph of the ring of all \(n\times n\) matrices over a finite field ⋮ On automorphism group of orthogonality graph of finite semisimple rings ⋮ Automorphism group of the intersection graph of ideals over a matrix ring ⋮ The automorphism group of the zero-divisor digraph of matrices over an antiring ⋮ Automorphisms of symplectic totally isotropic subspace inclusion graph ⋮ Automorphisms of the co-maximal ideal graph over matrix ring ⋮ Automorphisms of the zero-divisor graph of 2 × 2 matrix ring over ℤps ⋮ The automorphism group and fixing number of the orthogonality graph of the full matrix ring ⋮ Automorphism group of the total graph over a matrix ring ⋮ The automorphism group of zero-divisor graph of a finite semisimple ring ⋮ Nonlinear mappings on full matrices derivable at zero point ⋮ Automorphisms of the zero-divisor graph of the full matrix ring ⋮ Generators of the automorphism group of a regular graph over a ring ⋮ Automorphisms and domination numbers of transformation graphs over vector spaces ⋮ Automorphisms of the total graph over upper triangular matrices ⋮ Automorphism group of rank-decreasing graph of matrices ⋮ Nonlinear mappings on upper triangular matrices derivable at zero point ⋮ Automorphism group and fixing number of the orthogonality graph based on rank one upper triangular matrices ⋮ Automorphism group of the one-divisor graph over the semigroup of upper triangular matrices ⋮ Automorphism group of the subspace inclusion graph of a vector space ⋮ Nonlinear bijective maps on strictly upper triangular matrices preserving zero product ⋮ Automorphism group of an ideal-relation graph over a matrix ring ⋮ Automorphisms of the subgroup-relation graph over the group of unit upper triangular matrices ⋮ Automorphism Group of the Rank-decreasing Graph Over the Semigroup of Upper Triangular Matrices ⋮ End-regularity of zero-divisor graphs of group rings ⋮ Automorphisms of linear functional graphs over vector spaces ⋮ Automorphism group of the symmetry trace graph of real matrices

Cites Work

• The group of automorphisms of a zero-divisor graph based on rank one upper triangular matrices
• On the diameter and girth of a zero-divisor graph
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• Beck's coloring of a commutative ring
• Zero-divisor graphs, von Neumann regular rings, and Boolean algebras.
• On zero-divisor graphs of finite rings.
• On directed zero-divisor graphs of finite rings
• The diameter of a zero divisor graph
• THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING
• THE ZERO-DIVISOR GRAPH UNDER GROUP ACTIONS IN A NONCOMMUTATIVE RING
• Zero-Divisor Graphs of Matrices Over Commutative Rings
• THE ZERO-DIVISOR GRAPH OF VON NEUMANN REGULAR RINGS
• Zero-Divisor Graphs of Polynomials and Power Series Over Commutative Rings

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