Abstract
Let M be a module over a commutative ring, and let Spec(M) be the collection of all prime submodules of M. We topologize Spec(M) with Zariski topology, which is analogous to that for Spec(R), and for a nonempty subset T of Spec(M), we introduce a new graph G(τ T ), called the Zariski topology-graph. This graph helps us to study the algebraic (resp. topological) properties of M (resp. Spec(M)) by using the graph theoretical tools.
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