On the Genus of the Zero-Divisor Graph of Zn

Huadong Su, Pailing Li
2014 International Journal of Combinatorics  
Let R be a commutative ring with identity. The zero-divisor graph of R, denoted Γ(R), is the simple graph whose vertices are the nonzero zero-divisors of R, and two distinct vertices x and y are linked by an edge if and only if xy=0. The genus of a simple graph G is the smallest integer g such that G can be embedded into an orientable surface Sg. In this paper, we determine that the genus of the zero-divisor graph of Zn, the ring of integers modulo n, is two or three.
doi:10.1155/2014/390732 fatcat:gc2nrrajpvaf3bn7vwzc7ro5ci