### 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 | |

State | Published - Jan 1 2007 |

### Keywords

- Zero-divisor graphs

### ASJC Scopus subject areas

- Algebra and Number Theory

## Fingerprint Dive into the research topics of 'Infinite planar zero-divisor graphs'. Together they form a unique fingerprint.

## Cite this

Smith, N. O. (2007). Infinite planar zero-divisor graphs.

*Communications in Algebra*,*35*(1), 171-180. https://doi.org/10.1080/00927870601041458