In this paper we continue our study of perpendicular graph of modules, that was introduced in Hokkaido. 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 _ (M) to M with vertices M_=\ (0) A M\;|\; (0) B M \; 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 _ (M) . We study the clique number and chromatic number of _ (M) . We prove that if (_ (M) ) < and M has a simple submodule, then (_ (M) ) < . Among other results, it is shown that for a semi-simple module M, (_ (R M) ) = (_ (R M) ) .
SHIRALI et al. (Sun,) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: