TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Open Access ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Freq.: MONTHLY - Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Fuzzy non-adjacency vertex topological spaces associated with undirected fuzzy graphs

* ,

* Corresponding author · click or hover a name for details

pp. 1067–1074Vol. 29Issue 5-AMay 2026DOI: 10.47974/JIM-2285XML
Received:
01 May 2025
Published Online:
27 Jun 2026
Article type:
Research Article
Language:
EN
Article no.:
JIM-2285
Pages:
1067–1074

Abstract

This study introduces the novel fuzzy topology for undirect fuzzy graphs, that named “fuzzy non-adjacent vertex topology”. This topology clearly highlights non-adjacency relations, which are frequently eclipsed by traditional adjacency-centric models in fuzzy graph theory. The model builds on a relation that forms a sub-base for the new fuzzy topology by taking the vertex set and, for each vertex, specifying its non-adjacent ties to all other vertices in the fuzzy graph. After creating this new fuzzy topology and presenting the main examples of specific types of undirected fuzzy graphs, we studied and analyzed a number of properties associated with it and discussed them in an important context.

Keywords

Subject Classifications

05C7254A4068R10

References

[1] A. Rosenfeld, “Fuzzy graphs,” in Fuzzy Sets and Their Applications to Cognitive and Decision Processes, L. A. Zadeh, K. S. Fu, and M. Shimura, Eds. New York, USA: Academic Press, pp. 77–95 (1975).
[2] J. N. Mordeson and P. S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs, ser. Studies in Fuzziness and Soft Computing. Heidelberg, Germany: Physica-Verlag (2000).
[3] A. F. Hassan and Z. I. Abed, “Independent (non-adjacent vertices) topological spaces associated with undirected grapℎs, with some applications in biomathematics,” Journal of Physics: Conference Series, vol. 1591, no. 1, p. 012096 (2020), doi: 10.1088/1742-6596/1591/1/012096.
[4] F. Formato, G. Gerla, and L. Scarpati, “Fuzzy subgroups and similarities,” Soft Computing, vol. 3, no. 1, pp. 1-6 (1999), doi: 10.1007/s005000050085.
[5] A. Ali and A. F. Hassan, “The independent incompatible edges topology on di-grapℎs,” Journal of Physics: Conference Series, vol. 2322, no. 1, p. 012010 (2022), doi: 10.1088/1742-6596/2322/1/012010.
[6] H. Mutab, “Fuzzy grpℎs,” Journal of Advances in Mathematics, vol. 17, pp. 232-247 (2019), doi: 10.24297/jam.v17i0.8443.
[7] C. L. Chang, “Fuzzy topological spaces,” Journal of Mathematical Analysis and Applications, vol. 24, no. 1, pp. 182-190 (1968), doi: 10.1016/0022-247X(68)90057-7.
[8] M. Atef, A. E. F. El-Atik, and A. S. Nawar, “Fuzzy topological structures via fuzzy grapℎs and their applications,” Soft Computing, vol. 25, no. 8, pp. 6013-6027 (2021), doi: 10.1007/s00500-021-05594-8.
[9] A. M. Alzubaidi and M. Dammak, “Grapℎic topology on fuzzy grapℎs,” Advances in Mathematics: Scientific Journal, vol. 11, no. 10, pp. 853-868 (2022), doi: 10.37418/amsj.11.10.4.
[10] P. S. Gholap and V. E. Nikumbh, “Fuzzy topological spaces on fuzzy grpaℎs,” Annals of fuzzy Mathematics and Informatics, vol. 25, no. 3, pp. 279-291 (2023), doi: 10.30948/afmi.2023.25.3.279.
[11] P. S. Gholap, V. E. Nikumbh, and P. G. Andhare, “fuzzy topological spaces generated by fuzzy di grapℎs,” New Mathematics and Natural Computation, pp. 1-16 (2024), doi: 10.1142/S1793005725500401.
[12] S. Sarmad and Y. Y. Yousif, “Supre rough membership relations and supra fuzzy digrapℎs on related topologies,” Iraqi Journal of Science, vol. Special Issue, pp. 28-34 (2020), doi: 10.24996/ijs.2020.SI.1.5.
[13] F. G. Arenas, “Alexandroff spaces,” Acta Mathematica Universitatis Comenianae, vol. 68, no. 1, pp. 17-25 (1999).

Views: 24Downloads: 6Citations: 0