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Fuzzy magic labeling of simple graphs

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Abstract

The study of labeling graphs exposed to various distance constraints is motivated by the problem of minimizing the span of non-interfering frequencies assigned to radio transmitters. However, fuzzy labeling models yield more precision, flexibility and compatibility to the system compared to the classical models. In this paper we show that whether any simple graph is fuzzy magic labelizing, by considering the concept of fuzzy magic labeling of graphs. In fact, we prove that every connected graph is a fuzzy magic labelizing graph. Finally, we give some applications for fuzzy magic labeling graphs.

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References

  1. Akram, M., Waseem, N.: Novel applications of bipolar fuzzy graphs to decision making problems. J. Appl. Math. Comput. 56(1–2), 73–91 (2018)

    Article  MathSciNet  MATH  Google Scholar 

  2. Avadayappan, S., Jeyanthi, P., Vasuki, R.: Super magic strength of a graph. Indian J. Pure Appl. Math. 32(11), 1621–1630 (2001)

    MathSciNet  MATH  Google Scholar 

  3. Borzooei, R.A., Rashmanlou, H.: Cayley interval-valued fuzzy graphs. U.P.B. Sci. Bull. Ser. A 78(3), 83–94 (2016)

    MathSciNet  MATH  Google Scholar 

  4. Borzooei, R.A., Rashmanlou, H., Samantac, S., Pal, M.: A study on fuzzy labeling graphs. J. Intell. Fuzzy Syst. 30, 3349–3355 (2016)

    Article  MATH  Google Scholar 

  5. Chartrand, G., Zhang, P.: Chromatic Graph Theory. CRC Press, Taylor & Francis Group, Boca Raton (2009)

    MATH  Google Scholar 

  6. Gani, A.N., Akram, M., Subahashini, D.R.: Novel properties of fuzzy labeling graphs. J. Math. 375135, 1–6 (2014)

    Article  MathSciNet  Google Scholar 

  7. Gani, A.N., Subahashini, D.R.: Properties of fuzzy labeling graph. Appl. Math. Sci. 6(70), 3461–3466 (2012)

    MathSciNet  MATH  Google Scholar 

  8. Kotzing, A., Rosa, A.: Magic valuation of finite graphs. Can. Math. Bull. 13, 451–461 (1970)

    Article  MathSciNet  Google Scholar 

  9. Mathew, S., Mordeson, J.N., Malik, D.S.: Fuzzy Graph Theory. Springer, Berlin (2018)

    Book  MATH  Google Scholar 

  10. Ngurah, A.A.G., Salman, A.N.M., Susilowati, L.: H-Supermagic labeling of graphs. Discrete Math. 310(8), 1293–1300 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  11. Rashmanlou, H., Borzooei, R.A.: New concepts of fuzzy labeling graphs. Int. J. Appl. Comput. Math. 3(1), 173–184 (2017)

    Article  MathSciNet  Google Scholar 

  12. Rashmanlou, H., Pal, M., Samanta, S., Borzooei, R.A.: Product of bipolar fuzzy graphs and their degree. Int. J. Gen. Syst. 45(1), 1–14 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  13. Rosa, A.: On certain valuations of the vertices of a graph. In: Proceeding of the International Symposium on Theory of Graphs, Rome, Italy (1966)

  14. Rosenfield, A.: Fuzzy Sets and Their Applications, pp. 77–95. Academic Press, New York (1975)

    Google Scholar 

  15. Sarwar, M., Akram, M.: Novel concepts of bipolar fuzzy competition graphs. J. Appl. Math. Comput. 54(1–2), 511–547 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  16. Sahoo, S., Akram, M.: Intuitionistic fuzzy tolerance graphs with application. J. Appl. Math. Comput. 55(1–2), 495–511 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  17. Sunitha, M.S., Vijaya Kumar, A.: Complement of a fuzzy graph. Indian J. Pure Appl. Math. 33(9), 1451–1464 (2002)

    MathSciNet  MATH  Google Scholar 

  18. Stewart, B.M.: Supermagic complete graphs. Can. J. Math. 9, 427–438 (1966)

    Article  MathSciNet  MATH  Google Scholar 

  19. Trenkler, M.: Some results on magic graphs. In: Proceedings of the Third Czechoslovak Symposium on Graph Theory, Leipzig, pp. 328–332 (1983)

  20. Wang, Q., Zhan, J., Borzooei, R.A.: A study on soft rough semigroups and corresponding decision making applications. Open Math. 15, 1400–1413 (2017)

    MathSciNet  MATH  Google Scholar 

  21. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

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Acknowledgements

The authors wish to express their appreciation for several excellent suggestions for improvements in this paper made by the referees.

Funding

Funding information provided by Shahid Beheshti University.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematics, Payame Noor University, Tehran, Iran

    M. Fathalian & M. Hamidi

  2. Department of Mathematics, Shahid Beheshti University, Tehran, Iran

    R. A. Borzooei

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  1. M. Fathalian
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  2. R. A. Borzooei
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  3. M. Hamidi
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Correspondence to R. A. Borzooei.

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Fathalian, M., Borzooei, R.A. & Hamidi, M. Fuzzy magic labeling of simple graphs. J. Appl. Math. Comput. 60, 369–385 (2019). https://doi.org/10.1007/s12190-018-01218-x

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  • DOI: https://doi.org/10.1007/s12190-018-01218-x

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