Perpendicular graph of modules

Let R be a ring and M be an R-module. Two modules A and B are called orthogonal, written A⊥ B, if they do not have non-zero isomorphic submodules. We associate a graph Γ_(M) to M with vertices M⊥=\(0)≠ A≤ M ∃ B≠ (0) \;such that\; A⊥ B\, and for distinct A,B∈ M⊥, the vertices A and B are adjacent if and only if A⊥ B. The main object of this article is to study the interplay of module-theoretic properties of M with graph-theoretic properties of Γ_(M). An algorithm is given to generate perpendicular graphs of Zₙ.