Classification of Rings with Genus One Zero-Divisor Graphs
This paper investigates properties of the zero-divisor graph of a commutative ring and its genus. In particular, we determine all isomorphism classes of finite commutative rings with identity whose zero-divisor graph has genus one.
finite commutative ring, zero divisor, zero-divisor graph
Wickham, Cameron. "Classification of rings with genus one zero-divisor graphs." Communications in Algebra® 36, no. 2 (2008): 325-345.
Communications in Algebra