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A Study on Topological Indices in Fuzzy Graphs with Application in Decision Making Problems
Saeed Kosari, Xiaoli Qiang, Janusz Kacprzyk, Qura Tul Ain and Hossein Rashmanlou
Fuzzy graphs (FGs) are efficient mathematical models for analyzing many problems of daily life. Various problems in the fields of physics, telecommunication science, psychology and genetics can be modeled and solved with the help of fuzzy graph theory. One of the most widely used types of FG is vague graph (VG). VGs play an important role in various fields such as computer science, psychology, medicine, and political sciences and are used to find effective people in an organization or social institution. Today, connectivity indices are used in computer networks and economics to find the most suitable place for construction. These indices also have many applications in medical sciences, including ultrasound and radiology. Hence, in this research, we introduce connectivity index (CI), average connectivity index (ACI), and randic index (RI) in VGs with some examples. Likewise, some new vertices such as enhancing vertex (EV), reducing vertex (RV), and neutral vertex (NV) are described. Finally, an application of CI in the selecting town for building a school is given.
Keywords: Fuzzy graph, connectivity, vague set, vague graph, randic index, neutral vertex
Mathematics Subject Classification: 05C99, 03E72.