Fuzzy magic labeling of simple graphs

  • M. Fathalian
  • R. A. BorzooeiEmail author
  • M. Hamidi
Original Research


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.


Fuzzy graph Fuzzy labeling Fuzzy magic labeling Fuzzy magic labeling 

Mathematics Subject Classification

05C78 05C62 05C72 



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


Funding information provided by Shahid Beheshti University.


  1. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Avadayappan, S., Jeyanthi, P., Vasuki, R.: Super magic strength of a graph. Indian J. Pure Appl. Math. 32(11), 1621–1630 (2001)MathSciNetzbMATHGoogle Scholar
  3. 3.
    Borzooei, R.A., Rashmanlou, H.: Cayley interval-valued fuzzy graphs. U.P.B. Sci. Bull. Ser. A 78(3), 83–94 (2016)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Borzooei, R.A., Rashmanlou, H., Samantac, S., Pal, M.: A study on fuzzy labeling graphs. J. Intell. Fuzzy Syst. 30, 3349–3355 (2016)CrossRefzbMATHGoogle Scholar
  5. 5.
    Chartrand, G., Zhang, P.: Chromatic Graph Theory. CRC Press, Taylor & Francis Group, Boca Raton (2009)zbMATHGoogle Scholar
  6. 6.
    Gani, A.N., Akram, M., Subahashini, D.R.: Novel properties of fuzzy labeling graphs. J. Math. 375135, 1–6 (2014)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Gani, A.N., Subahashini, D.R.: Properties of fuzzy labeling graph. Appl. Math. Sci. 6(70), 3461–3466 (2012)MathSciNetzbMATHGoogle Scholar
  8. 8.
    Kotzing, A., Rosa, A.: Magic valuation of finite graphs. Can. Math. Bull. 13, 451–461 (1970)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Mathew, S., Mordeson, J.N., Malik, D.S.: Fuzzy Graph Theory. Springer, Berlin (2018)CrossRefzbMATHGoogle Scholar
  10. 10.
    Ngurah, A.A.G., Salman, A.N.M., Susilowati, L.: H-Supermagic labeling of graphs. Discrete Math. 310(8), 1293–1300 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Rashmanlou, H., Borzooei, R.A.: New concepts of fuzzy labeling graphs. Int. J. Appl. Comput. Math. 3(1), 173–184 (2017)MathSciNetCrossRefGoogle Scholar
  12. 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)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 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)Google Scholar
  14. 14.
    Rosenfield, A.: Fuzzy Sets and Their Applications, pp. 77–95. Academic Press, New York (1975)Google Scholar
  15. 15.
    Sarwar, M., Akram, M.: Novel concepts of bipolar fuzzy competition graphs. J. Appl. Math. Comput. 54(1–2), 511–547 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  16. 16.
    Sahoo, S., Akram, M.: Intuitionistic fuzzy tolerance graphs with application. J. Appl. Math. Comput. 55(1–2), 495–511 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Sunitha, M.S., Vijaya Kumar, A.: Complement of a fuzzy graph. Indian J. Pure Appl. Math. 33(9), 1451–1464 (2002)MathSciNetzbMATHGoogle Scholar
  18. 18.
    Stewart, B.M.: Supermagic complete graphs. Can. J. Math. 9, 427–438 (1966)MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Trenkler, M.: Some results on magic graphs. In: Proceedings of the Third Czechoslovak Symposium on Graph Theory, Leipzig, pp. 328–332 (1983)Google Scholar
  20. 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)MathSciNetzbMATHGoogle Scholar
  21. 21.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefzbMATHGoogle Scholar

Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of MathematicsPayame Noor UniversityTehranIran
  2. 2.Department of MathematicsShahid Beheshti UniversityTehranIran

Personalised recommendations