Advertisement

Certain fuzzy graph structures

  • Muhammad AkramEmail author
  • Muzzamal Sitara
Original Research
  • 37 Downloads

Abstract

A fuzzy graph structure is an extension of a fuzzy graph. In this research paper, we present certain notions, including semi strong min-product of fuzzy graph structures, regular fuzzy graph structures, strong and complete fuzzy graph structures. Moreover, we discuss degree and total degree of a vertex in semi strong min-product of fuzzy graph structures and investigate some of their properties. Furthermore, we present an application of fuzzy graph structures in decision-making, that is, identification of best traveling service. In last, we develop an algorithm explaining general procedure of our application.

Keywords

Graph structure Semi strong Degree Total degree Regular Decision-making Algorithm 

Mathematics Subject Classification

03E72 05C72 05C78 05C99 

Notes

References

  1. 1.
    Akram, M., Akmal, R., Alshehri, N.: On \(m\)-polar fuzzy graph structures. SpringerPlus (2016).  https://doi.org/10.1186/s40064-016-3066-8
  2. 2.
    Akram, M., Alshehri, N., Akmal, R.: Certain concepts in m-polar fuzzy graph structures. Discrete Dyn. Nat. Soc. (2016).  https://doi.org/10.1155/2016/5859080
  3. 3.
    Akram, M., Luqman, A.: A new decision-making method based on bipolar neutrosophic directed hypergraphs. J. Appl. Math. Comput. 57(1–2), 547–575 (2018)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Akram, M.: \(m\)-Polar Fuzzy Graphs: Theory, Methods & Applications, Studies in Fuzziness and Soft Computing 371, pp. 1–284. Springer, Berlin (2019)Google Scholar
  5. 5.
    Bhattacharya, P.: Some remarks on fuzzy graphs. Pattern Recognit. Lett. 6(5), 297–302 (1987)CrossRefzbMATHGoogle Scholar
  6. 6.
    Dinesh, T.: A study on graph structures, incidence algebras and their fuzzy analogues. Ph.D.thesis, Kannur University, Kannur, India (2011)Google Scholar
  7. 7.
    Harinath, P., Lavanya, S.: Fuzzy graph structures. Int. J. Appl. Eng. Res. 10, 70–74 (2015)Google Scholar
  8. 8.
    Kauffman, A.: Introduction a la Theorie des Sous-emsembles Flous 1. Masson et Cie, Paris (1973)Google Scholar
  9. 9.
    Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs. Physica Verlag, Heidelberg (2000). ISBN 978-3-7908-1854-3Google Scholar
  10. 10.
    Mordeson, J.N., Chang-Shyh, P.: Operations on fuzzy graphs. Inf. Sci. 79, 159–170 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Nagoor Gani, A., Radha, K.: On regular fuzzy graphs. J. Phys. Sci. 12, 33–44 (2008)zbMATHGoogle Scholar
  12. 12.
    Nagoor Gani, A., Radha, K.: The degree of a vertex in some fuzzy graphs. Int. J. Algorithms Comput. Math. 2(3), 107–116 (2009)zbMATHGoogle Scholar
  13. 13.
    Ramakrishnan, R.V., Dinesh, T.: On generalised fuzzy graph structures. Appl. Math. Sci. 5(4), 173–180 (2011)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Ramakrishnan, R.V., Dinesh, T.: On generalised fuzzy graph structures II. Adv. Fuzzy Math. 6(1), 5–12 (2011)zbMATHGoogle Scholar
  15. 15.
    Ramakrishnan, R.V., Dinesh, T.: On generalised fuzzy graph structures III. Bull. Kerala Math. Assoc. 8(1), 57–66 (2011)MathSciNetzbMATHGoogle Scholar
  16. 16.
    Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and their Applications, pp. 77–95. Academic Press, New York (1975)Google Scholar
  17. 17.
    Sampathkumar, E.: Generalized graph structures. Bull. Kerala Math. Assoc. 3(2), 65–123 (2006)MathSciNetGoogle Scholar
  18. 18.
    Sunitha, M.S., Vijayakumar, A.: Complement of a fuzzy graph. Indian J. Pure Appl. Math. 33(9), 1451–1464 (2002)MathSciNetzbMATHGoogle Scholar
  19. 19.
    Shahzadi, S., Akram, M.: Intuitionistic fuzzy soft graphs with applications. J. Appl. Math. Comput. 55(12), 369–392 (2017)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Sunitha, M.S., Vijayakumar, A.: A characterization of fuzzy trees. Inf. Sci. 113(9), 293–300 (1999)MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Zadeh, L.A.: Fuzzy sets. Inf. Control 8(3), 338–353 (1965)CrossRefzbMATHGoogle Scholar
  22. 22.
    Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3(2), 177–200 (1971)MathSciNetCrossRefzbMATHGoogle Scholar
  23. 23.
    Zhan, J., Masood, H., Akram, M.: Novel decision-making algorithms based on intuitionistic fuzzy rough environment. Int. J. Mach. Learn. Cybernet. (2018).  https://doi.org/10.1007/s13042-018-0827-4
  24. 24.
    Zhan, J., Akram, M., Sitara, M.: Novel decision-making method based on bipolar neutrosophic information. Soft Comput. (2018).  https://doi.org/10.1007/s00500-018-3552-8

Copyright information

© Korean Society for Computational and Applied Mathematics 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of the PunjabLahorePakistan

Personalised recommendations