On Soft Graph Isomorphism

The soft set theory provides a flexible framework for dealing with uncertain and imprecise information that is not adequately handled by classical set theory. The notion of a soft set was utilized to introduce the concept of a soft graph, which enables the generation of various representations of a relation represented by a graph through parameterization. Graph isomorphism is a key technique for pattern matching in various fields, such as image processing, computer and information systems, social network analysis, chemical bond exploration, and protein structure analysis. In this study, we explore isomorphism in soft graphs and investigate the properties of tabular representations of two isomorphic soft graphs. Additionally, we explore the concept of the soft complement of a soft graph and prove that it is a soft graph of the complement of the original graph. We also establish that if two soft graphs are isomorphic, their soft complements are also isomorphic. Moreover, we define self-complementary soft graphs and examine their properties.