On zero-divisor graphs of small finite commutative rings Original Research Article

In this article, all graphs on image vertices which can be realized as the zero-divisor graphs of a commutative rings with 1, and the list of all rings (up to isomorphism) which produce these graphs, are given. An algorithm is presented to find (up to isomorphism) all commutative, reduced rings with 1 which give rise to a zero-divisor graph on n vertices for any image. Also, the zero-divisor graph of a finite commutative ring is used to find bounds on the size of that ring.