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Interval Valued Fuzzy Graph and Complement Number

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Computational Sciences - Modelling, Computing and Soft Computing (CSMCS 2020)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1345))

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Abstract

In this paper, we present an example to show that many non-isomorphic IVFGs may have a same complement. To overcome this limitation, we introduce the notion of complement number of an edge and prove that given a complement IVFG \(\bar{G}\) along with its complement numbers, the IVFG for which \(\bar{G}\) acts as the complement can be uniquely determined. We also study the range of variation of complement number and some of its properties.

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References

  1. Akram, M., Dudek, W.A.: Interval valued fuzzy graphs. Comput. Math. Appl. 61(2), 289–299 (2011)

    Article  MathSciNet  Google Scholar 

  2. AL-Hawary, T.: Complete fuzzy graphs. Int. J. Math. Comb. 4, 26–34 (2011)

    Google Scholar 

  3. Tresa, S.D.M., Daise, S.D.M., Fernandez, S.: A study onclassic and non-classic interval valued fuzzy graphs. In: Proceedings of the International Conference on Mathematics 2018, pp. 72–77 (2018)

    Google Scholar 

  4. Tresa, S.D.M., Daise, S.D.M., Fernandez, S.: Classic and nonclassic interval valued fuzzy graphs. Int. J. Appl. Eng. Res. 13(3), 1–4 (2018)

    Google Scholar 

  5. Tresa, S.D.M., Daise, S.D.M., Fernandez, S.: On complement of interval valued fuzzy graphs. Int. J. Current Adv. Res. 7(5), 12954–56 (2018)

    Google Scholar 

  6. Tresa, S.D.M., Daise, S.D.M., Fernandez, S.: The lattice of pre-complements of a classic interval valued fuzzy graph. Malaya J. Matematik, 8, 1311–1320 (2020)

    Google Scholar 

  7. Deo, N.: Graph Theory with Applications to Engineering and Computer Science. PHI Learning Pvt. Ltd., Delhi (2014)

    MATH  Google Scholar 

  8. Hongmei, J., Lianhua, W.: Interval-valued fuzzy subsemigroups and subgroups associated by interval-valued fuzzy graphs. In: Global Congress on Intelligent Systems, pp. 484–487 (2009)

    Google Scholar 

  9. Mordeson, J.N., Peng, C.S.: Operation on fuzzy graphs. Inf. Sci. 19, 159–170 (1994)

    Article  MathSciNet  Google Scholar 

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

    Book  Google Scholar 

  11. Mathew, S., Sunitha, M.S.: Node connectivity and arc connectivity of a fuzzy graph. Inf. Sci. 180(4), 519–531 (2010)

    Article  MathSciNet  Google Scholar 

  12. Mathew, S., Sunitha, M.S.: Cycle connectivity in fuzzy graphs. J. Intell. Fuzzy Syst. 24(3), 549–554 (2013)

    Article  MathSciNet  Google Scholar 

  13. Pramanik, T., Samanta, S., Pal, M.: Interval-valued fuzzy planar graphs. Int. J. Mach. Learn. Cybern. 7(4), 653–664 (2014). https://doi.org/10.1007/s13042-014-0284-7

    Article  Google Scholar 

  14. Rashmanlou, H., Borzooei, R.A., Samanta, S., Pal, M.: Properties of interval valued intuitionistic (S, T)–fuzzy graphs. Pacific Sci. Rev. A Nat. Sci. Eng. 18(1), 30–37 (2016)

    Article  Google Scholar 

  15. Rosenfeld, A.: Fuzzy graphs, Fuzzy sets and their applications to cognitive and decision processes, pp. 77–95 (1975)

    Google Scholar 

  16. Samanta, S., Pal, M.: Fuzzy tolerance graphs. Int. J. Latest Trend Math. 1, 57–67 (2011)

    Google Scholar 

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

    Google Scholar 

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

    Google Scholar 

  19. Samanta, S., Pal, M.: Bipolar fuzzy hyper graphs. Int. J. Fuzzy Logic Syst. 2, 17–28 (2012)

    Article  Google Scholar 

  20. Samanta, S., Pal, M.: Fuzzy K-Competition graphs and P-Competition fuzzy graphs. Fuzzy Eng. Inf. 5, 191–204 (2013)

    Article  MathSciNet  Google Scholar 

  21. Samanta, S., Pal, M.: New concepts of fuzzy planar graph. Int. J. Adv. Res. Artif. Intell. 3, 52–59 (2014)

    Google Scholar 

  22. Samanta, S., Pal, M., Akram, M.: m-step fuzzy competition graphs. J. Appl. Math. Comput. 47, 461–472 (2015)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  24. Sunitha, M.S., Vijayakumar, A.: Complement of fuzzy graphs. Indian J. Pure and Appl. Math. 33, 1451–1464 (2002)

    MathSciNet  MATH  Google Scholar 

  25. Talebi, A. A., and Rashmanlou. H., Isomorphism on interval-valued fuzzy graphs. Ann. Fuzzy Math. Inform. 6(1), 47–58 (2013)

    Google Scholar 

  26. Talebi, A.A., Rashmanlou, H., Sadati, S.H.: Interval valued intuitionistic fuzzy competition graph. J. Mult. Valued Logic Soft Comput. 34, 5 (2020)

    Google Scholar 

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

    Article  Google Scholar 

  28. Zadeh, L.A.: The concept of a linguistic and application to approximate reasoning. Inf. Sci. 8(3), 199–249 (1975)

    Article  MathSciNet  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics, St. Albert’s College (Autonomous), Kochi, Kerala, India

    Deepthi Mary Tresa Souriar & Divya Mary Daise Souriar

  2. Department of Mathematics, Cochin University of Science and Technology, Kochi, Kerala, India

    Shery Fernandez

Authors
  1. Deepthi Mary Tresa Souriar
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  2. Divya Mary Daise Souriar
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  3. Shery Fernandez
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Editor information

Editors and Affiliations

  1. National Institute of Technology Calicut, Kozhikode, Kerala, India

    Ashish Awasthi

  2. National Institute of Technology Calicut, Kozhikode, Kerala, India

    Sunil Jacob John

  3. National Institute of Technology Calicut, Kozhikode, Kerala, India

    Satyananda Panda

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Souriar, D.M.T., Souriar, D.M.D., Fernandez, S. (2021). Interval Valued Fuzzy Graph and Complement Number. In: Awasthi, A., John, S.J., Panda, S. (eds) Computational Sciences - Modelling, Computing and Soft Computing. CSMCS 2020. Communications in Computer and Information Science, vol 1345. Springer, Singapore. https://doi.org/10.1007/978-981-16-4772-7_15

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  • DOI: https://doi.org/10.1007/978-981-16-4772-7_15

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-16-4771-0

  • Online ISBN: 978-981-16-4772-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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