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Graph theory plays crucial role in structuring many real-world problems including, medical sciences, control theory, expert systems and network security. Product in graphs, an operation that consider two graphs and produce a new graph by simple or complex changes, has wide range of applications in games theory, automata theory, structural mechanics and networking system. An intuitionistic fuzzy model is used to handle the vagueness and uncertainty in network problems. A Pythagorean fuzzy model is a powerful tool for describing vagueness and uncertainty more accurately as compared to intuitionistic fuzzy model. The objective of this paper is to apply the concept of Pythagorean fuzzy sets to graphs and then combine two Pythagorean fuzzy graphs (PFGs) using two new graph products namely, maximal product and the residue product. This research paper investigates the regularity for these products …