2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/164972Let $R$ 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.Revision and correction of Table 2. To appear in Houston Journal of MathematicsCommutative AlgebraCombinatorics13A99; 05C10; 13M99text