Table of Contents
International Journal of Combinatorics
Volume 2014, Article ID 390732, 5 pages
http://dx.doi.org/10.1155/2014/390732
Research Article

On the Genus of the Zero-Divisor Graph of

1School of Mathematical Sciences, Guangxi Teachers Education University, Nanning, Guangxi 530023, China
2School of Mathematical Sciences, Guangxi Teachers Education University, Nanning 530023, China

Received 1 February 2014; Accepted 6 July 2014; Published 22 July 2014

Academic Editor: Laszlo A. Szekely

Copyright © 2014 Huadong Su and Pailing Li. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let be a commutative ring with identity. The zero-divisor graph of , denoted , is the simple graph whose vertices are the nonzero zero-divisors of , and two distinct vertices and are linked by an edge if and only if . The genus of a simple graph is the smallest integer such that can be embedded into an orientable surface . In this paper, we determine that the genus of the zero-divisor graph of , the ring of integers modulo , is two or three.