Infinite planar zero-divisor graphs

Research output: Contribution to journalArticle

14 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)171-180
Number of pages10
JournalCommunications in Algebra
Volume35
Issue number1
DOIs
StatePublished - Jan 1 2007

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Zero-divisor Graph
Commutative Ring
Planar graph
Zero-divisor
Undirected Graph
Distinct

Keywords

  • Zero-divisor graphs

ASJC Scopus subject areas

  • Algebra and Number Theory

Cite this

Infinite planar zero-divisor graphs. / Smith, Neal O.

In: Communications in Algebra, Vol. 35, No. 1, 01.01.2007, p. 171-180.

Research output: Contribution to journalArticle

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