The Development of New Operations for Tensor Products of Product Fuzzy Graphs, Strong Product Fuzzy Graphs, and Complete Product Fuzzy Graphs
DOI:
https://doi.org/10.31851/sainmatika.v22i2.20347Keywords:
complete graph, fuzzy graph, product fuzzy graph, strong graph, tensor productAbstract
The purpose of this study is to develop new properties of product fuzzy graphs in the form of tensor product operations. The research method used consists of a preliminary stage, a stage of defining and theorems, a stage of proving theorems and verifying research results. The results of this study obtained the definition of tensor product operations from fuzzy graph products. Furthermore, it was found that the graph resulting from tensor product operations is a fuzzy graph, the tensor product operations of strong product fuzzy graphs are strong, and the tensor product operations of complete product fuzzy graphs are strong.
References
Akram, M., Habib, A., Ilyas, F., & Mohsan Dar, J. (2018). Specific Types of Pythagorean Fuzzy Graphs and Application to Decision-Making. Mathematical and Computational Applications, 23(3). https://doi.org/10.3390/mca23030042
Akram, M., Sitara, M., & Saeid, A. B. (2020). Residue product of fuzzy graph structures. Journal of Multiple-Valued Logic and Soft Computing, 34(3–4).
Al-Hawary, T., & Hourani, B. (2016). On product fuzzy graphs. Annals of Fuzzy Mathematics and Informatics, 12(2), 279–294.
Bharathi, T., & Leo, S. (2023). Distance in plithogenic product fuzzy graphs. Proyecciones, 42(6), 1521–1536. https://doi.org/10.22199/issn.0717-6279-5556
Dogra, S. (2015). Different Types of Product of Fuzzy Graphs. In Progress in Nonlinear Dynamics and Chaos (Vol. 3, Issue 1).
Farhang, N., & Talebi, Y. (2024). Novel Concepts In Vague Incidence Graphs With Application. Turkish World Mathematical Society Journal of Applied and Engineering Mathematics, 14(1), 336–352.
Firmansah, F., & Bayu, S. (2012). Graf Fuzzy Produk. Jurnal Matematika, 14(3).
Firmansah, F., Tasari, T., & Yuwono, M. R. (2025). The development of cartesian product operation of product fuzzy graphs and its properties. Desimal: Jurnal Matematika, 8(2), 207–214. https://doi.org/10.24042/djm
Javaid, M., Kashif, A., & Rashid, T. (2020). Hesitant Fuzzy Graphs and Their Products. Fuzzy Information and Engineering, 12(2), 238–252. https://doi.org/10.1080/16168658.2020.1817658
Josy, A., Mathew, S., & Mordeson, J. N. (2022). Neighborhood connectivity index of a fuzzy graph and its application to human trafficking. Iranian Journal of Fuzzy Systems, 19(3).
Mahalakshmi, L. (2024). Operations on Complex Intuitionistic Fuzzy Graph. International Journal for Research in Applied Science and Engineering Technology, 12(3). https://doi.org/10.22214/ijraset.2024.58864
Mohamed, S. Y., & Ali, A. M. (2021). Complement of max product of intuitionistic fuzzy graphs. Complex and Intelligent Systems, 7(6). https://doi.org/10.1007/s40747-021-00438-2
Muhiuddin, G., Pramanik, T., Alanazi, A. M., Mahboob, A., & Pal, M. (2022). Independent Fuzzy Graph: A New Approach. Proceedings of the National Academy of Sciences India Section A - Physical Sciences, 92(3). https://doi.org/10.1007/s40010-022-00769-w
Ramaswamy, V., & Poornima, B. (2009). Product Fuzzy Graphs. IJCSNS International Journal of Computer Science and Network Security, 9(1), 114–118.
Rosenfeld, A. (1975). Fuzzy Graphs. Fuzzy Sets and Their Applications, 77–95.
Shubatah, M. M. ., & Haifa, A. A. (2023). The Global Domination Number In Product Fuzzy Graphs. International Journal of Mathematics and Statistics, 6(1). https://doi.org/10.53555/eijms.v6i1.45
Zhu, B., & Xu, Z. (2016). Extended hesitant fuzzy sets. Technological and Economic Development of Economy, 22(1), 100–121. https://doi.org/10.3846/20294913.2014.981882
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Sainmatika: Jurnal Ilmiah Matematika dan Ilmu Pengetahuan Alam
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
