### 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) |
---|---|

Pages (from-to) | 1-32 |

Number of pages | 32 |

Journal | Houston Journal of Mathematics |

Volume | 36 |

Issue number | 1 |

State | Published - May 10 2010 |

### Fingerprint

### Keywords

- Planar
- Toroidal
- Zero-divisor graphs

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Houston Journal of Mathematics*,

*36*(1), 1-32.

**Commutative rings with toroidal zero-divisor graphs.** / Chiang-Hsieh, Hung Jen; Smith, Neal O; Wang, Hsin J.U.

Research output: Contribution to journal › Article

*Houston Journal of Mathematics*, vol. 36, no. 1, pp. 1-32.

}

TY - JOUR

T1 - Commutative rings with toroidal zero-divisor graphs

AU - Chiang-Hsieh, Hung Jen

AU - Smith, Neal O

AU - Wang, Hsin J.U.

PY - 2010/5/10

Y1 - 2010/5/10

N2 - 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.

AB - 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.

KW - Planar

KW - Toroidal

KW - Zero-divisor graphs

UR - http://www.scopus.com/inward/record.url?scp=77951870374&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77951870374&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77951870374

VL - 36

SP - 1

EP - 32

JO - Houston Journal of Mathematics

JF - Houston Journal of Mathematics

SN - 0362-1588

IS - 1

ER -