Infinite Planar Zero-Divisor Graphs

Neal O. Smith

doi:10.1080/00927870601041458

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JOURNAL ARTICLE

Infinite Planar Zero-Divisor Graphs

Neal O. Smith

Year: 2006 Journal: Communications in Algebra Vol: 35 (1)Pages: 171-180 Publisher: Taylor & Francis

DOI: 10.1080/00927870601041458

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Abstract

Given a commutative ring R, one can associate with R an undirected graph Γ(R) whose vertices are the nonzero zero-divisors of R, and two distinct vertices x and y are joined by an edge iff xy = 0. In this article, we determine precisely those planar graphs that can be realized as Γ(R) when R is an infinite commutative ring.

Keywords:

Mathematics Zero divisor Commutative ring Combinatorics Zero (linguistics) Planar graph Commutative property Planar Ring (chemistry) Graph Undirected graph Discrete mathematics Enhanced Data Rates for GSM Evolution

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Rings, Modules, and Algebras

Physical Sciences → Mathematics → Algebra and Number Theory

Advanced Topics in Algebra

Physical Sciences → Mathematics → Algebra and Number Theory

Algebraic structures and combinatorial models

Physical Sciences → Mathematics → Geometry and Topology

Infinite Planar Zero-Divisor Graphs

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