Infinite Planar Zero-Divisor Graphs

DOI10.1080/00927870601041458zbMath1107.13009OpenAlexW2026690647MaRDI QIDQ3430271

Neal O. Smith

Publication date: 21 March 2007

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

Full work available at URL: https://doi.org/10.1080/00927870601041458

Mathematics Subject Classification ID

Structural characterization of families of graphs (05C75) General commutative ring theory (13A99)

Related Items

When is the annihilating ideal graph of a zero-dimensional semiquasilocal commutative ring planar? Nonquasilocal case, Unnamed Item, A characterization of rings whose unitary Cayley graphs are planar, Graph of Linear Transformations Over $$\mathbb {R}$$, When is the complement of the zero-divisor graph of a commutative ring planar?, On zero-divisor graphs of commutative rings without identity, Classification of rings with projective zero-divisor graphs, On the genus of the zero-divisor graph of \(\mathbb Z_n\), On the genus of generalized unit and unitary Cayley graphs of a commutative ring, The total graph of a commutative ring, NILPOTENT FINITE RINGS WITH PLANAR ZERO-DIVISOR GRAPHS, Classification of non-local rings with genus two zero-divisor graphs, Commutative Rings Whose Zero-Divisor Graphs Have Positive Genus, A survey on genus of selected graphs from commutative rings

Cites Work

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• The zero-divisor graph of a commutative ring
• Beck's coloring of a commutative ring
• When a zero-divisor graph is planar or a complete \(r\)-partite graph
• The zero-divisor graph of a commutative semigroup
• Zero-divisor graphs, von Neumann regular rings, and Boolean algebras.
• Properties of rings with a finite number of zero divisors
• Properties of rings with a finite number of zero divisors. II
• CYCLES AND SYMMETRIES OF ZERO-DIVISORS
• THE ZERO-DIVISOR GRAPH OF VON NEUMANN REGULAR RINGS