Infinite planar zero-divisor graphs

Neal O. Smith

doi:10.1080/00927870601041458

Infinite planar zero-divisor graphs

Neal O. Smith

Mathematics

Research output: Contribution to journal › Article › peer-review

22 Scopus citations

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.

Original language	English (US)
Pages (from-to)	171-180
Number of pages	10
Journal	Communications in Algebra
Volume	35
Issue number	1
DOIs	https://doi.org/10.1080/00927870601041458
State	Published - Jan 2007

Keywords

Zero-divisor graphs

ASJC Scopus subject areas

Algebra and Number Theory

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10.1080/00927870601041458

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AB - 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.

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Infinite planar zero-divisor graphs

Abstract

Keywords

ASJC Scopus subject areas

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