Abstract
The fuzzy graph theory uses a substantial and important role in modelling and structuring many optimization problems. DIfferent type of uncertainties exist in most of the optimization problems in real lIfe scenarios due to indeterminate and incomplete information and it is a challenging task for the expert to design those optimization problems applying fuzzy graph. To design the incomplete, uncertainty and vagueness in graphical optimization problems, several extensions of graph theoretical ideas are proposed. The idea of neutrosophic graph plays an important role to manage the uncertainty, linked with the indeterminate and incomplete data/information of any optimization problem. In this manuscript, we present the idea of regular neutrosophic graph, strong neutrosophic graph, bipartite neutrosophic graph, regular neutrosophic graph, and regular strong neutrosophic graph. We also introduce six different operations on neutrosophic graph, viz., cartesian product, composition, join, direct product, lexicographic and strong product.
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