Topological numbers of fuzzy soft graphs and their application

Abstract

The diagram kind of a graph is used to show accumulated data. Graphs can be utilized for a variety of purposes because this data can be either quantitative or qualitative. Graphs can be used to model different relationships and processes in physical, biological, and social media marketing systems, and in finding directions on a map. A graph with properties attached to its nodes and edges that emphasize its applicability to real-world systems is sometimes called a network. The idea of fuzzy sets has developed in numerous ways and across many areas since its establishment in 1965. Applications of this theory can be found in numerous fields for instance in recognition of patterns, management science, AI, computer science, medicine, also in control engineering. The progress of mathematics has reached a very high level and continues now. While classical graph theory is widely applied in several domains, there are instances where its outcomes can be subject to uncertainty. In order to address this challenge, the utilization of the fuzzy theory of graphs is adopted, as it offers more accurate outcomes. There is a lack of a parameterization tool in fuzzy graph theory, as a consequence Molodtsov introduced soft set theory, which is a rather recent way to talk about ambiguity and vagueness. It is becoming more and more popular among scholars and is a novel approach to uncertainty and ambiguity simulation. The concept of soft graphs offers a parameterized perspective on graphs. In this article, we defined some familiar graph families in a fuzzy soft (FS) environment and by calculating their degrees, derived important results for two versions of Sombor numbers. In the end, we discussed an application of calculated results and by comparison, checked the efficiency of Sombor numbers in a FS framework.