Skip to main content
SpringerLink
Log in

Domination in fuzzy incidence graphs based on valid edges

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

Abstract

Fuzzy graph theory provides tools for modeling different types of real-world networks. However, we should consider more relations, especially the relationship between edges with their corresponding vertices, which usually refer to incidences, when external factors influence the real flow in a network. Then, fuzzy incidence graphs may sometimes model certain real-world situations better. The present study aims to define incidence valid edges, the recognition of which is easy, and their number is more than that of effective edges. In this regard, we introduce dominating sets in fuzzy incidence graphs by using incidence valid edges due to the importance of the concept of domination and its application in various issues. In addition, several important sets related to the dominating set such as independent and irredundant sets are investigated. Further, the concepts of domination, upper domination, and independent domination number, as well as independence, irredundant, and upper irredundant number in fuzzy incidence graphs are evaluated, along with their relation. Finally, an application of the concept of domination in a fuzzy incidence graph is obtained.

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

Similar content being viewed by others

References

  1. Ore, O.: Theory of Graphs. American Mathematical Society, Providence (1962)

    Book  Google Scholar 

  2. Berge, C.: Theory of Graphs and Its Applications. Methuen, London (1962)

    MATH  Google Scholar 

  3. Dinesh, T.: Fuzzy incidence graph-an introduction. Adv. Fuzzy Sets Syst. 21(1), 33–48 (2016)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  5. Rosenfeld, A.: Fuzzy graphs. In: Zadeh, L.A., Fu, K.S., Shimura, M. (eds.) Fuzzy Sets and their Applications to Cognitive and Decision Processes, pp. 77–95. Academic Press, New York (1975)

    Chapter  Google Scholar 

  6. Mordeson, J.N., Nair, P.S.: Fuzzy Graphs and Fuzzy Hypergraphs. Physica-Verly, Heidelberg (2000)

    Book  Google Scholar 

  7. Borzooei, R.A., Rashmanlou, H.: Dominating in vague graph and its applications. J. Intell. Fuzzy Syst. 29, 1933–1940 (2015)

    Article  Google Scholar 

  8. Borzooei, R.A., Rashmanlou, H.: Cayley interval-valued fuzzy graphs. UPB Sci. Bull. Ser. A: Appl. Math. Phys. 78(3), 83–94 (2016)

    MathSciNet  MATH  Google Scholar 

  9. Borzooei, R.A., Rashmanlou, H., Samanta, S., Pal, M.: A study on fuzzy labeling graphs. J. Intell. Fuzzy Syst. 30(6), 3349–3355 (2016)

    Article  Google Scholar 

  10. Rashmanlou, H., Borzooei, R.A.: Product vague graphs and its applications. J. Intell. Fuzzy Syst. 30(1), 371–382 (2016)

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  12. Akram, M.: m-Polar Fuzzy Graphs. Springer, Berlin (2019)

    Book  Google Scholar 

  13. Manjusha, O.T., Sunitha, M.S.: Coverings, matchings and paired domination in fuzzy graphs using strong arcs. Iran. J. Fuzzy Syst. 16(1), 145–157 (2019)

    MathSciNet  MATH  Google Scholar 

  14. Mordeson, J.N., Mathew, S.: Advanced Topics in Fuzzy Graph Theory. Springer, Berlin (2019)

    Book  Google Scholar 

  15. Chen, X.G., Sohn, M.Y., Ma, D.X.: Total efficient domination in fuzzy graphs. IEEE Access 7, 155405–155411 (2019)

    Article  Google Scholar 

  16. Mordeson, J.: Fuzzy incidence graphs. Adv. Fuzzy Sets Syst. 21(2), 121–133 (2016)

    Article  Google Scholar 

  17. Mathew, S., Mordeson, J.N.: Fuzzy influence graphs. New Math. Nat. Comput. 13(03), 311–325 (2017)

    Article  MathSciNet  Google Scholar 

  18. Mordeson, J.N., Mathew, S., Malik, D.S.: Fuzzy incidence graphs. In: Mordeson, J.N., Mathew, S., Malik, D.S. (eds.) Fuzzy Graph Theory with Applications to Human Trafficking, pp. 87–137. Springer, Cham (2018)

    Chapter  Google Scholar 

  19. Mathew, S., Mordeson, J., Yang, H.L.: Incidence cuts and connectivity in fuzzy incidence graphs. Iran. J. Fuzzy Syst. 16(2), 31–43 (2019)

    MathSciNet  MATH  Google Scholar 

  20. Akram, M., Sayed, S., Smarandache, F.: Neutrosophic incidence graphs with application. Axioms 7(3), 47 (2018)

    Article  Google Scholar 

  21. Akram, M., Ishfaq, N., Smarandache, F., Broumi, S.: Application of bipolar neutrosophic sets to incidence graphs. Neutrosophic Sets Syst. 27, 180–200 (2019)

    Google Scholar 

  22. Cockayne, E.J., Hedetniemi, S.T.: Independence graphs. In: Proceedings of 5th Southeast Conference on Combinatorics, Graph Theory and Computing, pp. 241–249. Utilitas Mathematica, Winnepeg (1974)

  23. Cockayne, E.J., Hedetniemi, S.: Towards a theory of domination in graphs. Networks 7(3), 247–261 (1977)

    Article  MathSciNet  Google Scholar 

  24. Bollobás, B., Cockayne, E.J.: Graph theoretic parameters concerning domination, independence, and irredundance. J. Gr. Theory 3(3), 241–249 (1979)

    Article  MathSciNet  Google Scholar 

  25. Cockayne, E.J., Favaron, O., Payan, C., Thomason, A.G.: Contributions to the theory of domination, independence and irredundance in graphs. Discrete Math. 33(3), 249–258 (1981)

    Article  MathSciNet  Google Scholar 

  26. Haynes, T., Hedetniemi, S.T., Slater, P.J.: Fundamentals of Domination in Graph. Marcel Deckker, New York (1998)

    MATH  Google Scholar 

  27. Somasundaram, A., Somasundaram, S.: Domination in fuzzy graphs-I. Pattern Recogn. Lett. 19, 787–791 (1998)

    Article  Google Scholar 

  28. Somasundaram, A.: Domination in products of fuzzy graphs. Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 13(2), 195–204 (2005)

    Article  MathSciNet  Google Scholar 

  29. Nagoor Gani, A., Chandrasekaran, V.T.: Domination in fuzzy graph. Adv. Fuzzy Sets Syst. 1(1), 17–26 (2006)

    MathSciNet  Google Scholar 

  30. Nagoor Gani, A., Vadivel, P.: On domination, independence and irredundance in fuzzy graph. Int. Rev. Fuzzy Math. 3(2), 191–198 (2008)

    MATH  Google Scholar 

  31. Natarajan, C., Ayyaswamy, S.K.: On strong (weak) domination in fuzzy graphs. Int. J. Math. Comput. Sci. 4(7), 1035–1037 (2010)

    MathSciNet  Google Scholar 

  32. Manjusha, O.T., Sunitha, M.S.: Strong domination in fuzzy graphs. Fuzzy Inf. Eng. 7(3), 369–377 (2015)

    Article  MathSciNet  Google Scholar 

  33. Parvathi, R., Thamizhendhi, G.: Domination in intuitionistic fuzzy graphs. Notes Intuit. Fuzzy Sets 16(2), 39–49 (2010)

    MATH  Google Scholar 

  34. Debnath, P.: Domination in interval-valued fuzzy graphs. Ann. Fuzzy Math. Inf. 6(2), 363–370 (2013)

    MathSciNet  MATH  Google Scholar 

  35. Karunambigai, M.G., Akram, M., Palanivel, K., Sivasankar, S.: Domination in bipolar fuzzy graphs. In: 2013 IEEE International Conference on Fuzzy Systems, (FUZZ-IEEE), pp. 1–6 (2013)

  36. Nazeer, I., Rashid, T., Guirao, J.L.G.: Domination of Fuzzy Incidence Graphs with Application in COVID-19 Testing Facility, Universidad De Murcia (2020)

  37. Rao, Y., Kosari, S., Shao, Z., Cai, R., Xinyue, L.: A study on domination in vague incidence graph and its application in medical sciences. Symmetry 12(11), 1885 (2020)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Central Tehran Branch, Islamic Azad University, Tehran, Iran

    S. Afsharmanesh

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

    R. A. Borzooei

Authors
  1. S. Afsharmanesh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. R. A. Borzooei
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to R. A. Borzooei.

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

Afsharmanesh, S., Borzooei, R.A. Domination in fuzzy incidence graphs based on valid edges. J. Appl. Math. Comput. 68, 101–124 (2022). https://doi.org/10.1007/s12190-021-01510-3

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s12190-021-01510-3

Keywords

Mathematics Subject Classification

Search

Navigation