On Soft Graph Isomorphism

Rajesh K. Thumbakara (), Jinta Jose () and Bobin George
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Rajesh K. Thumbakara: Department of Mathematics, Mar Athanasius College (Autonomous), Kothamangalam, Kerala, India
Jinta Jose: Department of Science and Humanities, Viswajyothi College of Engineering and Technology, Vazhakulam, Kerala, India
Bobin George: Department of Mathematics, Pavanatma College, Murickassery, Kerala, India

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 01, 113-129

Abstract: 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.

Keywords: Soft set; soft graph; soft graph isomorphism (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500073

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