Bounds of Extreme Energy of an Intuitionistic Fuzzy Directed Graph

  • B. Praba
  • G. DeepaEmail author
  • V. M. Chandrasekaran
  • Krishnamoorthy Venkatesan
  • K. Rajakumar
Conference paper
Part of the Trends in Mathematics book series (TM)


We are considering the website network of the web navigation of the customers. This website network can be representing as an intuitionistic fuzzy directed graph by means of considering the navigation of the customers. In this intuitionistic fuzzy directed graph, the links are considering as vertices and the path between the links are considering as edges. The weightage of each edge are considering as number of visitors getting the link from one link to another link (membership value), number of visitors not getting the link, i.e. under traffic from one link to another link (non-membership value) and drop off case (intuitionistic fuzzy index). For this graph we are determining the maximum, minimum energies and its upper, lower bounds.


Energy of a graph Energy of a fuzzy graph Energy of an intuitionistic fuzzy graph 



I wish to thank my co-authors for their kind help and support in my research work throughout this paper. My heartfelt thanks to my institution for providing me infrastructural facilities and excellent resources to carry out my research in VIT University, Vellore.


  1. 1.
    Anjali, N., Mathew, S.: Energy of a fuzzy graph. AFMI. 6, 455–465 [2013]Google Scholar
  2. 2.
    Atanassov, K.: Intuitionistic fuzzy sets: theory and applications. Heidelberg, New York, Physica-Verlag [1999]Google Scholar
  3. 3.
    Brankov, V., Stevanovic, D., Gutman, I.: Equienergetic chemical trees. J. Seb. Chem. Soc. 69, 549–553 [2004]CrossRefGoogle Scholar
  4. 4.
    Chandrashekar, A., Smitha, M.: On maximum degree energy of a graph. Int. J. Contemp. Math. Sciences. 4(8), 385–396 [2009]Google Scholar
  5. 5.
    Chountas, P., Alzebdi, M.S., Shannon, A., Atanassov, K.: On intuitionistic fuzzy trees. 13thICIFS, Sofia, NIFS. 15(2), 30–32 [2009]Google Scholar
  6. 6.
    Deepa, G., Praba, B., Chandrasekaran, V.M.: Max-Min intuitionistic fuzzy matrix of an intuitionistic fuzzy graph. IJPAM 98(3), 375–387 [2015]Google Scholar
  7. 7.
    Gutman, I.: The energy of a graph. Ber. Math-Statist. Sekt. Forschungsz. Graz. 103, 1–22 [1978]Google Scholar
  8. 8.
    Gutman, I.: The energy of graph: old and new results. Betten, A., Kohnert, A., Laue, R., Wassermann A. [Eds.], Algebraic Combinatorics and Applications. Springer-Verlag, Berlin, 196–211 [2001]Google Scholar
  9. 9.
    Gutman, I., Polansky, O.E.: Mathematical concepts in organic chemistry. Springer-Verlag, Berlin [1986]Google Scholar
  10. 10.
    Koolen, J.H., Moulton, V., Gutman, I.: Improving the McClelland inequality for total π-electron energy. Chemical physics Letters. 320, 213–216 [2000]CrossRefGoogle Scholar
  11. 11.
    McAllister, M.L.N.: Fuzzy introduction graphs. Comput. Math. Applic. 15(10), 871–886 [1988]Google Scholar
  12. 12.
    Mordeson, J.N.: Fuzzy line graphs. Pattern Recognition Letters. 14(5), 381–384, [1993]CrossRefGoogle Scholar
  13. 13.
    Praba, B., Chandrasekaran, V.M., Deepa, G.: Energy of an intuitionistic fuzzy graph. Italian journal of pure and applied mathematics. 32, 431–444 [2014]Google Scholar
  14. 14.
    Shannon, A., Atanassov, K.: On a generalization of intuitionistic fuzzy graphs. NIFS. 12(1), 24–29 [2006]Google Scholar
  15. 15.
    Yeh, R.T., Bang, S.Y.: Fuzzy relations, fuzzy graphs and their applications to clustering analysis, cognitive and decision processes in fuzzy sets, Zadeh, L.A., Fu, K.S., Shimara, M.Eds, Academic Press, New York, 125–149, [1975]Google Scholar

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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • B. Praba
    • 1
  • G. Deepa
    • 2
    Email author
  • V. M. Chandrasekaran
    • 2
  • Krishnamoorthy Venkatesan
    • 3
  • K. Rajakumar
    • 4
  1. 1.SSN College of EngineeringChennaiIndia
  2. 2.School of Advanced SciencesVIT UniversityVelloreIndia
  3. 3.College of Natural SciencesArba Minch UniversityArba MinchEthiopia
  4. 4.SCOPE, VIT UniversityVelloreIndia

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