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Let $R$ be a ring with unity. The cozero-divisor graph of a ring $R$, denotedby $\Gamma'(R)$, is an undirected simple graph whose vertices are the set ofall non-zero and non-unit elements of $R$, and two distinct vertices $x$ and$y$ are adjacent if and only if $x \notin Ry$ and $y \notin Rx$. In thisarticle, we extend some of the results of [24] to an arbitrary ring. In thisconnection, we derive a closed-form formula of the Wiener index of thecozero-divisor graph of a finite commutative ring $R$. As applications, wecompute the Wiener index of $\Gamma'(R)$, when either $R$ is the product ofring of integers modulo $n$ or a reduced ring. At the final part of this paper,we provide a SageMath code to compute the Wiener index of the cozero-divisorgraph of these class of rings including the ring $\mathbb{Z}_{n}$ of integersmodulo $n$.

Wiener index of the Cozero-divisor graph of a finite commutative ring