The automorphism group of the zero-divisor digraph of matrices over an antiring

DOI10.26493/1855-3974.2126.5b3zbMath1525.05076arXiv1908.04614MaRDI QIDQ6058493

Gabriel Verret, David Dolžan

Publication date: 1 November 2023

Published in: Ars Mathematica Contemporanea (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1908.04614

zbMATH Keywords

semiringzero-divisor graphautomorphism group of a graph

Mathematics Subject Classification ID

Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Semirings (16Y60) Directed graphs (digraphs), tournaments (05C20) Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.) (05C60)

Cites Work

• Automorphisms of the zero-divisor graph of the ring of all \(n\times n\) matrices over a finite field
• The group of automorphisms of a zero-divisor graph based on rank one upper triangular matrices
• A note on automorphisms of the zero-divisor graph of upper triangular matrices.
• Perfect zero-divisor graphs
• Invertible matrices and semilinear spaces over commutative semirings
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• The zero-divisor graph of a commutative semigroup
• Automorphisms of the zero-divisor graph of the full matrix ring
• THE GROUP OF GRAPH AUTOMORPHISMS OVER A MATRIX RING
• THE ZERO-DIVISOR GRAPHS OF RINGS AND SEMIRINGS
• An ideal based zero-divisor graph of a commutative semiring
• The zero-divisor graph with respect to ideals of a commutative semiring
• THE ZERO-DIVISOR GRAPH UNDER GROUP ACTIONS IN A NONCOMMUTATIVE RING
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