On Graph Structures in Fuzzy Environment Using Optimization Parameter

• Main Authors: Atiq Ur Rehman, Wojciech Salabun, Shahzad Faizi, Muhammad Hussain, Jaroslaw Watrobski
• Format: Article
• Language: English
• Published: IEEE 2021-01-01
• Series: IEEE Access
• Subjects: Fuzzy graph structure; weighted mean product; vertex degree; vertex total degree; regular fuzzy graph structure
• Online Access: https://ieeexplore.ieee.org/document/9435189/

This paper comprises the introduction of weighted mean products of fuzzy graph structures (<italic>FGSs</italic>) to construct weighted mean fuzzy graph structures (<italic>WMFGSs</italic>) with the help of optimization parameter, and establish some novel results after validating with examples, accordingly. The notions of regular and <inline-formula> <tex-math notation="LaTeX">$m\mu _{k}$ </tex-math></inline-formula>-regular <italic>FGSs</italic> are described, where <inline-formula> <tex-math notation="LaTeX">$m\in$ </tex-math></inline-formula>&#x005D;0, 1&#x005D; represents the degree of all vertices in <inline-formula> <tex-math notation="LaTeX">$\widetilde {G}$ </tex-math></inline-formula> under mapping <inline-formula> <tex-math notation="LaTeX">$\mu _{k}$ </tex-math></inline-formula>, and develop certain properties of regular <italic>WMFGSs</italic>. 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.