Wiener index and addressing of some finite graphs

Abstract

An addressing of length t of a graph G is an assignment of t-tuples with entries in 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 a simple graph whose vertex set is and two distinct vertices x and y are adjacent if and only if where are distinct primes greater than two and α, β are positive integers. Moreover, we estimate addressing of and obtain Wiener and Zagreb indices and some energies of it.