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Notion of Complex Pythagorean Fuzzy Graph with Properties and Application
Muhammad Shoaib, Saeed Kosari, Hossein Rashmanlou, M. Aslam Malik, Yongsheng Rao, Yahya Talebi and F. Mofidnakhaei

A Complex Pythagorean fuzzy set(CPFs) is an energetic mechanism for interpret the vague concepts more definitely. The CPFs-based models has more flexibility as compared to complex fuzzy models and intutionistic fuzzy models. The main goal of this paper is to introducing the concept of CPFs to graph theory in form of complex Pythagorean fuzzy graph. This work propose the notion of complex Pythagorean fuzzy graph (CPFG) and describes many techniques for their development. We then define properties namely caretesion product, composition, strong product, semi-strong product and direct product on CPFGs and prove them with examples. Related properties are also discussed in it. We will also present notion of strong complex Pythagorean fuzzy graph. We will also discuss self-complementary concept on complex pythagorean fuzzy graph. Finally, we will present application of CPFG.

Keywords: Cartesion products, composition, strong product, semi strong product and direct product of CPFG, strong CPFG of cartesion product and union of two CPFG, self complementary of CPFG, application of CPFG

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