Soft Semigraph Isomorphisms: Classification and Characteristics

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

New Mathematics and Natural Computation (NMNC), 2025, vol. 21, issue 02, 557-575

Abstract: A soft set is a mathematical tool designed for managing uncertainty. Semigraph is a generalization of a graph which is different from a hypergraph. Soft semigraph was introduced by applying the concept of soft set in semigraph. Through parameterization, soft semigraph generates a series of representations of a relationship given by a semigraph. Graph isomorphism serves as a crucial method for matching patterns in a range of areas including image processing, computer and information systems, social network analysis, exploration of chemical bonds, and analysis of protein structures. In this paper, we present various kinds of isomorphisms existing among soft semigraphs, namely, s-isomorphism, sev-isomorphism, se-isomorphism and sa-isomorphism. We prove that s-isomorphism between soft semigraphs is also sev-isomorphism. Moreover, we establish that sev and s-isomorphisms are also se-isomorphism and s, se and sev-isomorphisms are also sa-isomorphism. Through specific examples, we illustrate instances where the converse aspect of some of these results may not hold.

Keywords: Soft set; semigraph; soft semigraph (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1142/S1793005725500255

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