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Extension of Threshold Graphs Under Complex Fuzzy Environment

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Abstract

The prime objective of this paper is to introduce a new model of threshold graphs in the complex fuzzy environment that has the capability of handling two-dimensional vague data. The proposed model is called as complex fuzzy threshold graph (CFTG). We introduce certain concepts related to CFTGs including, complex fuzzy alternating 4-cycle, complex fuzzy threshold dimension and complex fuzzy partition number of complex fuzzy graphs. We illustrate these concepts with examples. Further, we investigate some of their properties and discuss proficiency of the presented approach by investigating potential applications related to water source controlling system and internet service providers.

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References

  1. Akram, M.: \(m\)-Polar fuzzy graphs, Studies in Fuzziness and Soft Computing. Springer 371,(2019)

  2. Akram, M.: Bipolar fuzzy graphs. Inf. Sci. 181(24), 5548–5564 (2011)

    Article  MathSciNet  Google Scholar 

  3. Akram, M., Davvaz, B.: Strong intuitionistic fuzzy graphs. Filomat 26(1), 177–196 (2012)

    Article  MathSciNet  Google Scholar 

  4. Akram, M., Dudek, W.A.: Interval-valued fuzzy graphs. Comput. Math. with Appl. 61(2), 289–299 (2011)

    Article  MathSciNet  Google Scholar 

  5. Akram, M., Nawaz, S.: Fuzzy soft graphs with applications. J. Intel. Fuzzy Syst. 30(6), 3619–3632 (2016)

    Article  Google Scholar 

  6. Andelic, M., Simic, S.K.: Some notes on the threshold graphs. Discerete Math. 310, 2241–2248 (2010)

    Article  MathSciNet  Google Scholar 

  7. Buckley, J.J.: Fuzzy complex numbers. Fuzzy Sets Syst. 33(3), 333–345 (1989)

    Article  MathSciNet  Google Scholar 

  8. Chvatal, V., Hammer, P.L.: Set-packing problems and threshold graphs , 73–21 (1973)

  9. Kauffmann, A.: Introduction a la theorie des Sous-emsembles Flous. Masson et Cie (1973)

  10. Mahadev, N.V., Peled, U.N.: Threshold graphs and related topics. North Holland 56, (1995)

  11. Mahaptra, T., Pal, M.: An investigation on m-polar fuzzy threshold graph and its application on resource power controlling system. Journal of Ambient Intelligence and Humanized Computing , 1–14 (2021)

  12. Makwana, R.M., Thakar, V.K., Chaulan, N.C.: Extraction of illumination invariant features using fuzzy threshold based approach. Int. J. Comput. Appl., 25–31 (2011)

  13. Morderson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs, vol. 1998, 2nd edn. Physica Verlag, Heidelberg (2001)

    Google Scholar 

  14. Nagoorgani, A., Malarvizhi, J.: Isomorphism properties of strong fuzzy graphs. Int. J. Algorithms Comput. Math. 2(1), 39–47 (2009)

    Google Scholar 

  15. Nagoorgani, A., Radha, K.: On regular fuzzy graphs. J. Phys. Sci. 12, 33–40 (2008)

    MATH  Google Scholar 

  16. Naggogani, A., Vadivel, P.: Relations between the parameters of independent domination and irredundance in fuzzy graph. Int. J. Algorithms Comput. Math. 2(1), 15–19 (2009)

    Google Scholar 

  17. Nagoorgani, A., Vijayalaakshmi, P.: Intensive arc in domination of fuzzy graph. Int. J. Contemp. Math. Sci. 6(26), 1303–1309 (2011)

    MathSciNet  Google Scholar 

  18. Nair, P.S.: Perfect and precisely perfect fuzzy graphs. Fuzzy Information Processing Society , 19–22 (2008)

  19. Nair, P.S., Cheng, S.C.: Cliques and fuzzy cliques in fuzzy graphs, IFSA World Congress and 20th NAFIPS. Int. Conf. 4, 2277–2280 (2001)

    Google Scholar 

  20. Nguyen, H.T., Kandel, A., Kreinovich, V.: Complex fuzzy sets: towards new foundations. Proc. Nineth IEEE Int. Conf. Fuzzy Syst. 2, 1045–1048 (2000)

    Google Scholar 

  21. Ordman, E.T.: Threshold coverings and resource allocation. Congressus Numerantium 49, 99–113 (1985)

    MathSciNet  MATH  Google Scholar 

  22. Pramanik, T., Pal, M., Mondal, S.: Interval valued fuzzy threshold graph. Pacific Sci. Rev. Nat. Sci. Eng. 18(1), 66–71 (2016)

    Article  Google Scholar 

  23. Ramot, D., Milo, R., Friedman, M., Kandel, A.: Complex fuzzy sets. IEEE Trans. Fuzzy Syst. 10(2), 171–186 (2002)

    Article  Google Scholar 

  24. Rosenfeld, A.: Fuzzy graphs. Fuzzy Sets and their Applications to Cognitive and Decision Processes Academic Press , 77–95 (1975)

  25. Samanta, S., Pal, M.: Fuzzy threshold graphs, CiiT. Int. J. Fuzzy Syst. 3, 1–9 (2011)

    Google Scholar 

  26. Samanta, S., Pal, M.: Fuzzy k-competition graphs and p-competition fuzzy graphs. Fuzzy Inf. Eng. 5, 191–204 (2013)

    Article  MathSciNet  Google Scholar 

  27. Samanta, S., Pal, M.: Fuzzy Planar Graphs. IEEE Trans. Fuzzy Syst. 23(6), 1936–1942 (2015)

    Article  Google Scholar 

  28. Samanta, S., Pramanik, T., Pal, M.: Fuzzy colouring of fuzzy graphs. Afrika Matematika 27, 37–50 (2016)

    Article  MathSciNet  Google Scholar 

  29. Samanta, S., Dubey, V.K., Sarkar, B.: Measure of influences in social networks. Appl. Soft Comput. 99, 106858 (2021)

    Article  Google Scholar 

  30. Tao, W., Jin, H., Zhang, Y., Liu, L., Wang, D.: Image thresholding using graph cuts. Syst. Humans 38(5), 1181–1195 (2008)

    Article  Google Scholar 

  31. Thirunavukarasu, P., Suresh, R., Viswanathan, K.K.: Energy of a complex fuzzy graph. Int. J. Math. Sci. Eng. Appl. 10(1), 243–248 (2016)

    Google Scholar 

  32. Yaqoob, N., Gulistan, M., Kadry, S., Wahab, H.A.: Complex intuitionistic fuzzy graphs with application in cellular network provider companies Mathematics 7(1), 35 (2019)

    Google Scholar 

  33. Yang, L., Mao, H.: Intitutionistic fuzzy threshold graphs. J. Intel. Fuzzy Syst. 36(6), 6641–6651 (2019)

    Article  Google Scholar 

  34. Yazdanbakhsh, O., Dick, S.: A systematic review of complex fuzzy sets and logic. Fuzzy Sets Syst. 338, 1–22 (2018)

    Article  MathSciNet  Google Scholar 

  35. Zadeh, L.A.: Fuzzy sets, Information. Control 8(3), 338–353 (1965)

    Article  MathSciNet  Google Scholar 

  36. Zhang, G., Dillon, T.S., Cai, K.Y., Ma, J.: Jie Lu, Operation properties and \(\delta \)-equalitues of complex fuzzy sets. Int. J. Approx. Reason. 50(8), 1227–1249 (2009)

    Article  Google Scholar 

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Acknowledgements

The authors are highly thankful to the honorable reviewers and editors of the Journal “International Journal of Applied and Computational Mathematics” for their suggestions to improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, P.O. Box No. 54590, Lahore, Pakistan

    Saira Hameed, Muhammad Akram & Noreen Mustafa

  2. Tamralipta Mahavidyalaya, Tamluk, West Bengal, 721636, India

    Sovan Samanta

Authors
  1. Saira Hameed
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  2. Muhammad Akram
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  3. Noreen Mustafa
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  4. Sovan Samanta
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First three authors conceptualized and represented the idea of the article while fourth author (S. Samanta) reviewed the article.

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Correspondence to Sovan Samanta.

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Hameed, S., Akram, M., Mustafa, N. et al. Extension of Threshold Graphs Under Complex Fuzzy Environment. Int. J. Appl. Comput. Math 7, 202 (2021). https://doi.org/10.1007/s40819-021-01138-8

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