Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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β-PRODUCT OF PRODUCT FUZZY GRAPHS

  • TALAL ALI AL-HAWARY (Department of Mathematics, Yarmouk University) ;
  • MAREF Y.M. ALZOUBI (Department of Mathematics, College of Sciences, Yarmouk University)
  • Received : 2022.12.09
  • Accepted : 2023.12.18
  • Published : 2024.03.30
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Abstract

In this article, a new operation on product fuzzy graphs (PFGs) is provide; namely β-product. We give sufficient conditions for the β-product of two PFGs to be strong and we prove if the β-product of two PFGs is complete, then one of them is strong. We also study the unbiased notion of the class of PFGs and necessary and sufficient conditions for the β-product to be unbiased are given.

Keywords

Acknowledgement

The authors thanks the referees for useful comments and suggestions that improved the paper.

References

  1. T. Al-Hawary, Characterizations of matroid via OFR-sets, Turkish Journal of Mathematics 25 (2001), 445-455.
  2. T. Al-Hawary, Complete fuzzy graphs, J. Math. Combinatorics 4 (2011), 26-34.
  3. T. Al-Hawary, Certain classes of fuzzy graphs, European J. Pure and Appl. Math. 10 (2012), 552-560.
  4. T. Al-Hawary, S. Al-Shalaldeh and M. Akram, Certain Matrices and Energies of fuzzy graphs, TWMS J. Pure Appl. and Math. 14 (2023), 50-68.
  5. T. Al-Hawary and L. Al-Momani, *-balanced fuzzy graphs, arXiv preprint arXiv:1804.08677, (2018), 26-34.
  6. T. Al-Hawary and B. Hourani, On intuitionistic product fuzzy graphs, Ital. J. Pure Appl. Math (2017), 113-126.
  7. T. Al-Hawary and B. Hourani, On product fuzzy graphs, Annals Fuzzy Math. Inform. 12 (2016), 279-294.
  8. T. Al-Hawary, Density Results for Perfectly Regular and Perfectly Edge-regular fuzzy graphs, Disc. Math. Scie. and Cryptography 2 (2022), 1-10.
  9. T. Al-Hawary, Maximal strong product and balanced fuzzy graphs, To appear in J. Appl. Math. and Informatics.
  10. T. Al-Hawary and M. Hashim, Semi-fuzzy graphs, To appear in Boletim da Sociedade Paranaense de Matematica.
  11. T. Al-Hawary, Strong Modular Product and Complete Fuzzy Graphs, To appear in Ital. J. Pure Appl.
  12. T. Al-Hawary, Complete Hamacher fuzzy graphs, J. Appl. Math. and Informatics 40 (2022), 1043-1052.
  13. M. Akram, D. Saleem, T. Al-Hawary, Spherical fuzzy graphs with application to decisionmaking, Math. and Comp. Appl. 25 (2020), 8-40.
  14. K.R. Bhutani, On automorphism of fuzzy graphs, Pattern Recognition Letter 9 (1969), 159-162. https://doi.org/10.1016/0167-8655(89)90049-4
  15. S. Dogra, Different types of product of fuzzy graphs, Prog. Nonlin. Dyn. Chaos 3 (2015), 41-56.
  16. J.N. Mordeson and C.S. Peng, Operations on fuzzy graphs, Information Sciences (1979), 381-3
  17. A. Nagoor Gani and B. Fathima Gani, Beta and Gamma product of fuzzy graphs, Inter. J. Fuzzy mathematical Archive 4 (2014), 20-36.
  18. S. Dogra, Different types of product of fuzzy graphs, Prog. Nonlin. Dyn. Chaos 3 (2015), 41-56.
  19. A. Nagoor Gani and J. Malarvizhi, Isomorphism on fuzzy graphs, Int. J. Comp. and Math. Sci. 2 (2008), 190-196.
  20. A. Nagoor Gani and J. Malarvizhi, Isomorphism properties on strong fuzzy graphs, Int. J. Algorithms, Comp. and Math. 2 (2009), 39-47.
  21. A. Nagoor Gani and K. Radha, On regular fuzzy graphs, J. Physical Sciences 12 (2008), 33-40.
  22. A. Rosenfeld, FGs, in Zadeh. L.A.K.S. Fu, K. Tanaka and M. Shirmura (Eds), Fuzzy sets and their applications to cognitive and processes, Academic Press, New York, 2008, 77-95.
  23. V. Ramaswamy and B. Poornima, Picture fuzzy graphs, Inter. J. Computer Sci. and Network Security 9 (2009), 114-124.
  24. M.S. Sunitha and A.V. Kumar, Complements of fuzzy graphs, Indian J. Pure Appl. Math. 33 (2002), 1451-1464.
  25. L.A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X