Skip to main content
SpringerLink
Log in

Generalized neutrosophic planar graphs and its application

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

Abstract

In the existing definition of a neutrosophic planar graph, there is a limitation. In that definition, the value of falsity in degree of planarity is 1, even then the crisp underline graph is planar. This limitation is removed in the proposed definition. In this study, an advanced concept of the neutrosophic planar graphs is given and investigated the generalized neutrosophic planar graphs (GNPG). The score of planarity is calculated based on the true, falsity and indeterminacy values of degree of planarity to measure the overall planarity of a GNPG. And a few related properties are investigated. A real-life application is presented and solved by this concept of a GNPG.

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

Similar content being viewed by others

References

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

    Google Scholar 

  2. 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 

  3. Samanta, S., Pal, M.: Fuzzy threshold graphs. CIIT Int. J. Fuzzy Syst. 3(12), 360–364 (2011)

    Google Scholar 

  4. Samanta, S., Pal, M.: Irregular bipolar FGs. Int. J. Appl. Fuzzy Sets 2, 91–102 (2012)

    Google Scholar 

  5. Mahapatra, R., Samanta, S., Pal, M., Qin, X.: RSM index: a new way of link prediction in social networks. J. Intell. Fuzzy Syst. 37, 2137–2151 (2019). https://doi.org/10.3233/JIFS-181452

    Article  Google Scholar 

  6. Mahapatra, R., Samanta, S., Allahviranloo, T., Pal, M.: Radio fuzzy graphs and assignment of frequency in radio stations. Comput. Appl. Math. 38, 117 (2019). https://doi.org/10.1007/s40314-019-0888-3

    Article  MathSciNet  MATH  Google Scholar 

  7. Mahapatra, R., Samanta, S., Pal, M.: Applications of edge colouring of fuzzy graphs. Informatica 31(2), 313–330 (2020). https://doi.org/10.15388/20-INFOR403

    Article  MathSciNet  Google Scholar 

  8. Smaradache, F.: Neutrosophy, Neutrosophic Probability, Set, and Logic. Pro Quest Information and Learning, Ann Arbor, Michigan (1998)

    Google Scholar 

  9. Broumi, S., Talea, M., Bakali, A., Smarandache, F.: Single valued neutrosophic graphs. J. New Theory 10, 86–101 (2016)

    Google Scholar 

  10. Akram, M., Shahzadi, G.: Operation on single-valued NGs. J. Uncertain Syst. 11(1), 1–26 (2017)

    Google Scholar 

  11. Samanta, S., Sarkar, B.: A study on generalized fuzzy grapgs. J. Intell. Fuzzy Syst. 35, 3405–3412 (2018)

    Article  Google Scholar 

  12. Samanta, S., Pal, M.: Fuzzy planar graphs. IEEE Trans. Fuzzy Syst. 23(6), 1936–1942 (2015)

    Article  Google Scholar 

  13. Akram, M.: Single-valued neutrosophic planer graph. Int. J. Algebr. Stat. 5, 157–167 (2016)

    Article  Google Scholar 

  14. Akram, M., Sitara, M.: Novel applications of single-valued neutrosophic graph structures in decision-making. J. Appl. Math. Comput. 56(1–2), 501–532 (2018)

    Article  MathSciNet  Google Scholar 

  15. Akram, M., Luqman, A.: A new decision-making method based on bipolar neutrosophic directed hypergraphs. J. Appl. Math. Comput. 57, 547–575 (2018)

    Article  MathSciNet  Google Scholar 

  16. Naz, S., Akram, M., Smarandache, F.: Certain notions of energy in single-valued neutrosophic graphs. Axioms 7(3), 50 (2018). https://doi.org/10.3390/axioms7030050

    Article  Google Scholar 

  17. Akram, M.: Single-Valued Neutrosophic Graphs, Infosys Science Foundation Series in Mathematical Sciences. Springer, Berlin (2018)

    Google Scholar 

  18. Smarandache, F.: Neutrosophic set-a generalization of the intuitionistic fuzzy set. In: IEEE International Conference on Granular Computing, 2006, pp. 38–42 (2006). https://doi.org/10.1109/GRC.2006.1635754

  19. Broumi, S., Bakali, A., Talea, M., Smarandache, F., Hassan, A.: Proceedings of the Annual Symposium of the Institution of Solid Mechanics and Session of the Commission of Acoustics, SISOM 2017 Bucharest 18–19 May

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, India

    Rupkumar Mahapatra & Madhumangal Pal

  2. Department of Mathematics, Tamralipta Mahavidyalaya, Tamluk, West Bengal, 721636, India

    Sovan Samanta

Authors
  1. Rupkumar Mahapatra
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sovan Samanta
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Madhumangal Pal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sovan Samanta.

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

Mahapatra, R., Samanta, S. & Pal, M. Generalized neutrosophic planar graphs and its application. J. Appl. Math. Comput. 65, 693–712 (2021). https://doi.org/10.1007/s12190-020-01411-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-020-01411-x

Keywords

Search

Navigation