Let $Γ(\mathbb{Z}_n)$ be the zero divisor graph of the commutative ring $\mathbb{Z}_n$ and $L(Γ(\mathbb{Z}_n))$ be the line graph of $Γ(\mathbb{Z}_n)$. In this paper, we discuss about the neighborhood of a vertex, the neighborhood number and the adjacency matrix of $L(Γ(\mathbb{Z}_n))$. We also study Wiener index and energy of $L(Γ(\mathbb{Z}_n))$, where $n=pq$, $p^2$ respectively for $p$ and $q$ are primes. Moreover, we give MATLAB coding of our calculations.