Wiener index and addressing of some finite graphs

AbstractAn addressing of length t of a graph G is an assignment of t-tuples with entries in [Formula: see text] called addresses, to the vertices of G such that the distance between any two vertices can be determined from their addresses. Let Z(R) be the set of zero-divisors of a commutative ring R. In this article, we investigate the adjacency matrix of [Formula: see text] a simple graph whose vertex set is [Formula: see text] and two distinct vertices x and y are adjacent if and only if [Formula: see text] where [Formula: see text] are distinct primes greater than two and α, β are positive integers. Moreover, we estimate addressing of [Formula: see text] and obtain Wiener and Zagreb indices and some energies of it.