Skip to main content
SpringerLink
Log in

Certain fuzzy graph structures

  • Original Research
  • Published:
Journal of Applied Mathematics and Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13

Similar content being viewed by others

References

  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. 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

    Article  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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. Bhattacharya, P.: Some remarks on fuzzy graphs. Pattern Recognit. Lett. 6(5), 297–302 (1987)

    Article  Google Scholar 

  6. Dinesh, T.: A study on graph structures, incidence algebras and their fuzzy analogues. Ph.D.thesis, Kannur University, Kannur, India (2011)

  7. Harinath, P., Lavanya, S.: Fuzzy graph structures. Int. J. Appl. Eng. Res. 10, 70–74 (2015)

    Google Scholar 

  8. Kauffman, A.: Introduction a la Theorie des Sous-emsembles Flous 1. Masson et Cie, Paris (1973)

    Google Scholar 

  9. Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs. Physica Verlag, Heidelberg (2000). ISBN 978-3-7908-1854-3

  10. Mordeson, J.N., Chang-Shyh, P.: Operations on fuzzy graphs. Inf. Sci. 79, 159–170 (1994)

    Article  MathSciNet  Google Scholar 

  11. Nagoor Gani, A., Radha, K.: On regular fuzzy graphs. J. Phys. Sci. 12, 33–44 (2008)

    MATH  Google Scholar 

  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)

    MATH  Google Scholar 

  13. Ramakrishnan, R.V., Dinesh, T.: On generalised fuzzy graph structures. Appl. Math. Sci. 5(4), 173–180 (2011)

    MathSciNet  MATH  Google Scholar 

  14. Ramakrishnan, R.V., Dinesh, T.: On generalised fuzzy graph structures II. Adv. Fuzzy Math. 6(1), 5–12 (2011)

    MATH  Google Scholar 

  15. Ramakrishnan, R.V., Dinesh, T.: On generalised fuzzy graph structures III. Bull. Kerala Math. Assoc. 8(1), 57–66 (2011)

    MathSciNet  MATH  Google Scholar 

  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. Sampathkumar, E.: Generalized graph structures. Bull. Kerala Math. Assoc. 3(2), 65–123 (2006)

    MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  19. Shahzadi, S., Akram, M.: Intuitionistic fuzzy soft graphs with applications. J. Appl. Math. Comput. 55(12), 369–392 (2017)

    Article  MathSciNet  Google Scholar 

  20. Sunitha, M.S., Vijayakumar, A.: A characterization of fuzzy trees. Inf. Sci. 113(9), 293–300 (1999)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  22. Zadeh, L.A.: Similarity relations and fuzzy orderings. Inf. Sci. 3(2), 177–200 (1971)

    Article  MathSciNet  Google Scholar 

  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

    Article  Google Scholar 

  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

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

    Muhammad Akram & Muzzamal Sitara

Authors
  1. Muhammad Akram
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Muzzamal Sitara
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Akram.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Akram, M., Sitara, M. Certain fuzzy graph structures. J. Appl. Math. Comput. 61, 25–56 (2019). https://doi.org/10.1007/s12190-019-01237-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-019-01237-2

Keywords

Mathematics Subject Classification

Search

Navigation