Path Fuzzy Bitopological Spaces on Fuzzy Directed Graphs

Authors

  • P. S. Gholap Department of Mathematics, Arts, Science and Commerce College (affiliated to Savitribai Phule Pune University), Rahuri 414705, Maharashtra, India https://orcid.org/0000-0002-0359-8736
  • V. E. Nikumbh Department of Mathematics, P. V. P. College of Arts, Science and Commerce (affiliated to Savitribai Phule Pune University), Pravaranagar, Ahmednagar 413713, Maharashtra, India https://orcid.org/0000-0003-0480-3698
  • P. G. Andhare Department of Mathematics, R. B. N. B. College (affiliated to Savitribai Phule Pune University), Shrirampur, Ahmednagar 413709, Maharashtra, India https://orcid.org/0009-0003-6134-1028
  • S. B. Gaikwad Department of Mathematics, New Arts, Commerce and Science College (affiliated to Savitribai Phule Pune University), Ahmednagar 414001, Maharashtra, India https://orcid.org/0000-0001-8394-0329

DOI:

https://doi.org/10.26713/cma.v15i3.2853

Keywords:

Path fuzzy topological space, Path fuzzy bitopological space, Fuzzy directed graph

Abstract

In this paper, we introduce a new concept of fuzzy topological spaces on fuzzy directed graphs by utilizing path relations between vertices and discuss several key results related to fuzzy topological spaces on various fuzzy digraphs. We define strongly connected, symmetric, and asymmetric fuzzy directed graphs, demonstrating that the associated path topological spaces are indiscrete. Furthermore, by employing path fuzzy topological spaces, we define a path fuzzy bitopological space associated with a fuzzy digraph. Various separation axioms, such as fuzzy pairwise \(T_{0}\), \(T_{1}\), \(T_{2}\) and fuzzy pairwise weakly \(T_{2}\), are studied for path fuzzy bitopological spaces, and the interrelations between path topological spaces and path fuzzy bitopological spaces are examined. This paper also initiates the concept of fuzzy bitopological spaces for fuzzy directed graphs.

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Published

30-11-2024
CITATION

How to Cite

Gholap, P. S., Nikumbh, V. E., Andhare, P. G., & Gaikwad, S. B. (2024). Path Fuzzy Bitopological Spaces on Fuzzy Directed Graphs. Communications in Mathematics and Applications, 15(3), 947–957. https://doi.org/10.26713/cma.v15i3.2853

Issue

Vol. 15 No. 3 (2024)

Section

Research Article

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