Let R be a ring with unity. The cozero-divisor graph of a ring R, denoted
by Ξβ²(R), is an undirected simple graph whose vertices are the set of
all non-zero and non-unit elements of R, and two distinct vertices x and
y are adjacent if and only if xβ/Ry and yβ/Rx. In this
article, we extend some of the results of [24] to an arbitrary ring. In this
connection, we derive a closed-form formula of the Wiener index of the
cozero-divisor graph of a finite commutative ring R. As applications, we
compute the Wiener index of Ξβ²(R), when either R is the product of
ring 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-divisor
graph of these class of rings including the ring Znβ of integers
modulo n