Rings whose zero-divisor graphs have positive genus
It is shown that, for a fixed positive integer g, there are finitely many isomorphism classes of rings whose zero-divisor graph has genus g. The proof can then be modified to yield an analogous result for nonorientable genus.
Wickham, Cameron. "Rings whose zero-divisor graphs have positive genus." Journal of Algebra 321, no. 2 (2009): 377-383.
Journal of Algebra