  In this article, explicit formulas for finding the determining number and the
metric dimension of the zero-divisor graph of Z_n and non-Boolean semisimple
rings are given. In the case of Boolean rings, an upper bound of the
determining number and the metric dimension of zero-divisor graph is
determined. Further, the determining number and the metric dimension of some
important graphs other than zero-divisor graphs, are proved and the open
problem by Boutin, regarding the determining number of graphs is settled.
