Characterizations of Three Classes of Zero-Divisor Graphs

The zero-divisor graph Γ( R ) of a commutative ring R is the graph whose vertices consist of the nonzero zero-divisors of R such that distinct vertices x and y are adjacent if and only if xy = 0. In this paper, a characterization is provided for zero-divisor graphs of Boolean rings. Also, commutative rings R such that Γ( R ) is isomorphic to the zero-divisor graph of a direct product of integral domains are classified, as well as those whose zero-divisor graphs are central vertex complete.