### Abstract

Let R be a commutative ring and let Γ(R) denote its zero-divisor graph. We investigate the genus number of the compact Riemann surface in which Γ(R) can be embedded and explicitly determine all finite commutative rings R (up to isomorphism) such that Γ(R) is either toroidal or planar.

Original language | English (US) |
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Pages (from-to) | 1-32 |

Number of pages | 32 |

Journal | Houston Journal of Mathematics |

Volume | 36 |

Issue number | 1 |

State | Published - May 10 2010 |

### Keywords

- Planar
- Toroidal
- Zero-divisor graphs

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Chiang-Hsieh, H. J., Smith, N. O., & Wang, H. J. U. (2010). Commutative rings with toroidal zero-divisor graphs.

*Houston Journal of Mathematics*,*36*(1), 1-32.