Let $mathbb{Z}^n$ be the Cartesian product of the set of integers $mathbb{Z}$ and let ($mathbb{Z}$, T) and ($mathbb{Z}^n$, $T^n$) be the Khalimsky line topology on $mathbb{Z}$ and the Khalimsky product topology on $mathbb{Z}^n$, respectively. Then for a set $X;{subset};mathbb{Z}^n$, consider the subspace (X, $T^n_X$) induced from ($mathbb{Z}^n$, $T^n$). Considering a k-adjacency on (X, $T^n_X$), we call it a (computer topological) space with k-adjacency and use the notation (X, k, $T^n_X$) := $X_{n,k}$. In this paper we introduce the notions of KD-($k_0$, $k_1$)-homotopy equivalence and KD-k-deformation retract and investigate a classification of (computer topological) spaces $X_{n,k}$ in terms of a KD-($k_0$, $k_1$)-homotopy equivalence.