  Graph theory has successfully used to solve a wide range of problems
encountered in diverse fields such as medical sciences, neural networks,
control theory, transportation, clustering analysis, expert systems, image
capturing, and network security. In past few years, a number of generalizations
of graph theoretical concepts have developed to model the impreciseness and
uncertainties in graphical network problems. A Pythagorean fuzzy set is a
powerful tool for describing the vague concepts more precisely. The Pythagorean
fuzzy set-based models provide more flexibility in handling the human judgment
information as compared to other fuzzy models. The objective of this paper is
to apply the concept of Pythagorean fuzzy sets to graph theory. This work
introduces the notion of Pythagorean fuzzy graphs (PFGs) and describes a number
of methods for their construction. We then define some basic operations on PFGs
and prove some of their important properties. The work also discusses the
notion of isomorphism between Pythagorean fuzzy graphs with a numerical
example. Further, we introduce the concept of the strong Pythagorean fuzzy
graph and the complete Pythagorean fuzzy graph. In addition, the paper also
proves some results on self-complementary, self-weak complementary with
Pythagorean fuzzy strong graphs and Pythagorean fuzzy complete graphs.
