On the Genus of the Zero-Divisor Graph of Zn

Abstract EN

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.