On the Harary index of $\Gamma(\mathbb{Z}_n)$

Abstract

In this work, the Harary index of zero-divisor graphs of rings $\mathbb{Z}_n$ are calculated when n is a member of the set {2p, p², p^\lambda, pq, p²q, pqr} where p, q and r are distinct prime numbers and $\lambda$ is an integer number. We give the formulas for computing the Harary index of $\Gamma(\mathbb{Z}_n)$. Moreover, the Harary index of graphs for products of rings was computed.