In this study, we introduce some new concepts related to single-valued neutrosophic graphs such as homomorphism, isomorphism, weak isomorphism and co-weak isomorphism, and define arithmetic Cartesian product, arithmetic direct product, and arithmetic lexicographical product operations on single-valued neutrosophic graphs with their examples. We also introduce intersection and union operations of single-valued neutrosophic graphs, and give some examples related to these operations. Furthermore we define two types of addition between two single-valued neutrosophic graphs based on union operation and summation operation of single valued neutrosophic numbers. Finally we present an application of single-valued neutrosophic graphs in decision making.
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