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Fuzzy Topological Spaces Generated by Fuzzy Digraphs

Author

Listed:
  • P. S. Gholap

    (Department of Mathematics, Arts Science and Commerce College, Rahuri, Maharashtra 413705, India)

  • V. E. Nikumbh

    (Department of Mathematics, PVP College of Arts, Science and Commerce, Pravaranagar, Maharashtra 413713, India)

  • P. G. Andhare

    (Department of Mathematics, RBNB College, Shrirampur, Maharashtra 413709, India)

Abstract

In this paper, we defined various fuzzy topological spaces on fuzzy digraph and study interrelation between them. Using adjacency relation on fuzzy vertices and fuzzy edges of fuzzy digraph we defined, namely two types of fuzzy topologies, left(right) fuzzy vertex topology and left(right) fuzzy edge topology on fuzzy digraph, respectively. We have obtained results related to fuzzy topology on fuzzy subdigraph H of fuzzy digraph G. Separation axioms T0, T1 and T2 for these fuzzy topological spaces are studied. Some characterization results for fuzzy topological spaces related to isomorphic fuzzy digraphs are given. Further, we have shown that two fuzzy digraphs are isomorphic if and only if their corresponding fuzzy topologies are homeomorphic, this relation on set of fuzzy digraphs forms an equivalence relation. We have also defined and studied fuzzy bitopological spaces on fuzzy digraphs.

Suggested Citation

  • P. S. Gholap & V. E. Nikumbh & P. G. Andhare, 2025. "Fuzzy Topological Spaces Generated by Fuzzy Digraphs," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 21(03), pages 823-838, November.
    • Handle: RePEc:wsi:nmncxx:v:21:y:2025:i:03:n:s1793005725500401
    DOI: 10.1142/S1793005725500401
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