Graph operations produce new classes of graphs from initial ones which in turn may be useful for the modeling and recognition of computer network designs. A Pythagorean fuzzy set-based model offers more flexibility to cope with human evaluation information as compared to intuitionistic fuzzy model. The main objective of this research study is to expand the area of discussion on Pythagorean fuzzy graphs by establishing fruitful results and notions related to an operation on Pythagorean fuzzy graphs called strong product. Certain concepts, including connectedness, completeness, regularity and partially regularity of strong product Pythagorean fuzzy graphs are discussed. It is shown that the strong product of two regular Pythagorean fuzzy graphs may not be regular. Moreover, some necessary and sufficient conditions for the strong product of two regular Pythagorean fuzzy graphs to be regular are established. Finally, an algorithm for Pythagorean fuzzy multi-criteria decision making is presented and problem concerning to evaluation of domestic airlines in Japan is solved to demonstrate the applicability of PFGs in realistic scenarios.
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