Commutative rings with toroidal zero-divisor graphs

2007/02/15 by Hung Jen Chiang-Hsieh, Chiang-Hsieh, Hung-Jen, Neal O. Smith +3 · 1 citation
Mathematics · #Finite Group Theory Research #Rings, Modules, and Algebras #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0702451

Abstract

Let R be a commutative ring and Γ(R) denote its zero-divisor graph. In this paper, we investigate the genus number of the compact Riemann surface which Γ(R) can be embedded and illustrate all finite commutative rings R (up to isomorphism) such that Γ(R) is either toroidal or planar.

Citations

• The Zero-Divisor Graph of a Commutative Ring

Cited by

• Power graphs of (non)orientable genus two

Related

• Rings whose total graphs have genus at most one
• When the Annihilator Graph of a Commutative Ring Is Planar or Toroidal?
• Genus of commuting graphs of some classes of finite rings
• Toroidal involutory Cayley graphs
• The Unit-Zero Divisor Graph of a Commutative Ring