Local Rings with Genus Two Zero Divisor Graph
To each commutative ring R we can associate a graph, the zero divisor graph of R, whose vertices are the zero divisors of R, and such that two vertices are adjacent if their product is zero. Presently, we enumerate the local finite commutative rings whose zero divisor graphs have orientable genus 2.
commutative algebra, finite rings, local rings, zero divisor graphs
Bloomfield, Nathan, and Cameron Wickham. "Local rings with genus two zero divisor graph." Communications in Algebra® 38, no. 8 (2010): 2965-2980.
Communications in Algebra