Co-normal products and modular products of soft graphs

Abstract

Most of our conventional tools for formal reasoning, computing, and modeling are precise, deterministic, and crisp. However, many complicated problems in the domains of economics, medicine, engineering, the environment, social science, and other disciplines demand data that is not always precise. We cannot always use traditional approaches because there are so many different types of uncertainty present in these problems. This difficulty could be caused by the parameterization tool’s insufficiency. Soft set theory, which Molodtsov presented in 1999, is a generic mathematical approach for handling uncertain data. Many researchers are currently using soft set theory to solve problems involving decision-making. The concept of soft graphs is used to provide a parameterized point of view for graphs. The topic of graph products has received a lot of interest in graph theory. It is a binary operation on graphs with numerous combinatorial uses. On soft graphs, we can define product operations in a manner similar to how graph products are defined. The co-normal product, the restricted co-normal product, the modular product, and the restricted modular product of soft graphs are all introduced in this study. We prove that these products of soft graphs are again soft graphs and derive methods for computing their vertex count, edge count, and the sum of part degrees.