On graph structures in fuzzy environment using optimization parameter

This paper comprises the introduction of weighted mean products of fuzzy graph structures (FGSs) to construct weighted mean fuzzy graph structures (WMFGSs) with the help of optimization parameter, and establish some novel results after validating with examples, accordingly. The notions of regular and mμk-regular FGSs are described, where m ∈]0, 1] represents the degree of all vertices in ~G under mapping μk, and develop certain properties of regular WMFGSs. In addition, we create a flowchart to present common application procedures of fuzzy graphical frameworks to classify the advanced city out of some important Pakistani cities subject to certain parameters.