Zero-divisor graphs of amalgamated duplication of a ring along an ideal

Abstract

Let $R$ be a commutative ring with identity and let $I$ be an ideal of $R$. Let $R\bowtie I$ be the subring of $R\times R$ consisting of the elements $(r,r+i)$ for $r\in R$ and $i\in I$. We study the diameter and girth of the zero-divisor graph of the ring $R\bowtie I$.

9 pages