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Soft Semigraph Isomorphisms: Classification and Characteristics

Author

Listed:
  • 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)

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.

Suggested Citation

  • Bobin George & Jinta Jose & Rajesh K. Thumbakara, 2025. "Soft Semigraph Isomorphisms: Classification and Characteristics," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 21(02), pages 557-575, July.
    • Handle: RePEc:wsi:nmncxx:v:21:y:2025:i:02:n:s1793005725500255
    DOI: 10.1142/S1793005725500255
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