On the Wiener index of prime graphs PG(ℤn)

A Prime Graph, denoted by [Formula: see text], is a graph associated with a ring [Formula: see text]. The vertices of [Formula: see text] correspond to the elements of the ring [Formula: see text], and two elements [Formula: see text] and [Formula: see text] are adjacent in [Formula: see text] if and only if [Formula: see text] or [Formula: see text]. In this paper, we explore the Wiener index of the prime graph for certain rings, specifically [Formula: see text], where [Formula: see text] and [Formula: see text].