Let R be a commutative ring with unity 1 and let G(V,E) be a simple graph. In this research article, we study the metric dimension in zero-divisor graphs associated with commutative rings. We show that for a given rational q∈(0,1), there exists a finite graph G such that the ratio $\frac{di{m}_M\left(G\right)}{\left|V\right(H\left)\right|}=q$, where H is any induced connected subgraph of G. We provide a metric dimension formula for a zero-divisor graph Γ(R×????_q) and give metric dimension of the zero-divisor graph $\Gamma (R_1\times R_2\times \cdots \times R_n)$, where $R_1,R_2,\dots ,R_n$ are n finite commutative rings with each having unity 1 and none of R_i, 1≤i≤n, being isomorphic to the Boolean ring ${\prod }_{i=1}^n{\mathbb{Z}}_2$. We discuss the metric dimension of Cartesian product of zero-divisor graphs and show that there exists a zero-divisor graph $\Gamma \left(R_1\right)\times \Gamma \left(R_2\right)$ such that $di{m}_M\left(\Gamma \right(R_1)\times \Gamma (R_2\left)\right)$ lies between the numbers $di{m}_M\left(\Gamma \right(R_1\left)\right)$ and $di{m}_M\left(\Gamma \right(R_1\left)\right)+1$, where R₁ and R₂ are any two finite commutative rings (not domains) with each having unity 1.

Given a commutative ring R with identity $1\ne 0$, let the set $Z\left(R\right)$ denote the set of zero-divisors and let $Z^{*}\left(R\right)=Z\left(R\right)\setminus \left\{0\right\}$ be the set of non-zero zero-divisors of R. The zero-divisor graph of R, denoted by $\Gamma \left(R\right)$, is a simple graph whose vertex set is $Z^{*}\left(R\right)$ and each pair of vertices in $Z^{*}\left(R\right)$ are adjacent when their product is 0. In this article, we find the structure and Laplacian spectrum of the zero-divisor graphs $\Gamma \left({\mathbb{Z}}_n\right)$ for $n=p^{N_1}{q}^{N_2}$, where $p<q$ are primes and $N_1,N_2$ are positive integers.