On Wiener Index of Unit Graph Associated with a Commutative Ring

Abstract

Let [Formula: see text] be a ring with non-zero identity. The unit graph of [Formula: see text], denoted by [Formula: see text], is an undirected graph with all the elements of [Formula: see text] as vertices and where distinct vertices [Formula: see text], [Formula: see text] are adjacent if and only if [Formula: see text] is a unit of [Formula: see text]. In this paper, we investigate the Wiener index and hyper-Wiener index of [Formula: see text] and explicitly determine their values.