On Realizing Zero-Divisor Graphs

DOI10.1080/00927870802182499zbMath1168.13004OpenAlexW2059029315MaRDI QIDQ5301516

John D. LaGrange

Publication date: 20 January 2009

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00927870802182499

zbMATH Keywords

Boolean ringszero-divisor graphsdirect products of integral domains

Mathematics Subject Classification ID

Graph theory (05C99) General commutative ring theory (13A99)

Related Items (16)

Zero-divisor graph of semisimple group-rings ⋮ The idempotent-divisor graphs of a commutative ring ⋮ Classifying annihilating-ideal graphs of commutative artinian rings ⋮ Zero divisor graphs of commutative graded rings ⋮ Some remarks on the compressed zero-divisor graph ⋮ Perfectness of \(G\)-generalized join of graphs ⋮ Induced subgraphs of zero-divisor graphs ⋮ Poset graphs and the lattice of graph annihilators ⋮ A Note on the Uniqueness of Zero-Divisor Graphs with Loops (Research) ⋮ Characterizations of connected orthogonality graphs of projections of Rickart ∗-rings ⋮ Invariants and isomorphism theorems for zero-divisor graphs of commutative rings of quotients ⋮ The Zero-Divisor Graph of a Commutative Semigroup: A Survey ⋮ Commutative Boolean monoids, reduced rings, and the compressed zero-divisor graph ⋮ Zero Divisor Graphs of Finite Direct Products of Finite Rings ⋮ Beck's coloring of finite product of commutative ring with unity ⋮ Annihilators in zero-divisor graphs of semilattices and reduced commutative semigroups

Cites Work

• Unnamed Item
• On zero-divisor graphs of small finite commutative rings
• On the diameter and girth of a zero-divisor graph
• Coloring of commutative rings
• The zero-divisor graph of a commutative ring
• Zero-divisor graphs, von Neumann regular rings, and Boolean algebras.
• On the zero-divisor graph of a commutative ring
• Complemented zero-divisor graphs and Boolean rings
• The diameter of a zero divisor graph
• CYCLES AND SYMMETRIES OF ZERO-DIVISORS
• THE ZERO-DIVISOR GRAPH OF VON NEUMANN REGULAR RINGS
• Zero-Divisor Graphs of Polynomials and Power Series Over Commutative Rings

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