The Girth of the Zero-Divisor Graph of the Direct Product of Commutative Rings 

Qiong LIU* 

Department of Mathematics, Shanghai University of Electric Power, Shanghai, CHINA 

Abstract: This electronic document is a “live” template. The various components of your paper [title, text, heads, etc.] are already defined on the style sheet, as illustrated by the portions given in this document. (Abstract) In this paper, we consider the zero-divisor graph of the direct product of commutative rings. Specifically, we give the equivalent characterization of the girth of the zero-divisor graph of R R 1 2 × , when thegirth is 3, 4, ｏｒ ∞ , where each Ri is a commutative ring for i = 1,2 . 

Keywords: Zero-divisor graph; Diameter; Girth; Commutative Rings