Complemented zero-divisor graphs and Boolean rings

For a commutative ring R, the zero-divisor graph of R is the graph whose vertices are the nonzero zero-divisors of R such that the vertices x and y are adjacent if and only if xy=0. In this paper, we classify the zero-divisor graphs of Boolean rings, as well as those of Boolean rings that are rationally complete. We also provide a complete list of those rings whose zero-divisor graphs have the property that every vertex is either an end or adjacent to an end.