Threshold Graphs Under Pythagorean Fuzzy Information

In this article, we present the concept of Pythagorean fuzzy threshold graphs (FTGs) which are generalizations of intuitionistic FTGs. We show that Pythagorean FTGs do not contain Pythagorean fuzzy alternating (FA) 4 - cycle. Pythagorean FTGs can be constructed by consecutively adding an isolated node or a dominating node. We propose that Pythagorean FTGs are Pythagorean fuzzy split graphs (SGs). Also threshold dimension and threshold partition number of Pythagorean fuzzy graphs (PFGs) and some basic theorems on threshold dimension and threshold partition number have been presented. Finally, we discuss the implementations of Pythagorean FTGs in the gas supply allocation problem and traffic flow problem. By means of implementations, we observe that Pythagorean FTGs are applicable to a greater extent than intuitionistic FTGs to deal with uncertainty and vagueness.