Fuzzy Incidence Graphs

  • John N. Mordeson
  • Sunil Mathew
  • Davender S. Malik
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 365)


We introduce the notion of the degree of incidence of a vertex and an edge in a fuzzy graph in fuzzy graph theory. We concentrate on incidence, where the edge is adjacent to the vertex. We determine results concerning bridges, cutvertices, cutpairs, fuzzy incidence paths, fuzzy incidence tree for fuzzy incidence graphs. In (Dinesh, Ph.D. thesis, Kannur University, Kerala, India, [4]; Dinesh, Adv Fuzzy Sets Syst, 21:33–48, 2016, [5]), Dinesh introduced the notion of the degree of incidence of a vertex and an edge in fuzzy graph theory. This notion seem to have potential use in a variety of areas involving networks, Mordeson (Adv Fuzzy Sets Syst, 22:121–133, 2016, [12]).


  1. 1.
    K.R. Bhutani, A. Rosenfeld, Strong arcs in fuzzy graphs. Inf. Sci. 152, 319–322 (2003)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    K.R. Bhutani, A. Rosenfeld, Fuzzy end notes in fuzzy graphs. Inf. Sci. 152, 323–326 (2003)CrossRefMATHGoogle Scholar
  3. 3.
    C. Caniglia, B. Cousino, S.-C. Cheng, D.S. Malik, J.N. Mordeson, Intuition fuzzy graphs: weakening and strengthening members of a group. J. Fuzzy Math. 24, 87–102 (2016)MATHGoogle Scholar
  4. 4.
    T. Dinesh, Ph.D. thesis, Kannur University, Kerala, IndiaGoogle Scholar
  5. 5.
    T. Dinesh, Fuzzy incidence graph - an introduction. Adv. Fuzzy Sets Syst. 21, 33–48 (2016)CrossRefMATHGoogle Scholar
  6. 6.
    N.E. Friedkin, E.C. Johnson, Social Influence Network Theory: A Sociological Examination of Small Group Dynamics. Structural Analysis in the Social Sciences, vol. 33 (Cambridge University Press, Cambridge, 2011)Google Scholar
  7. 7.
    H. Irfan, From India to the U. S. via the jungles of Guatemala: investigation exposes route taken by human traffickers, Daily Mail, India, 20 Jan 2012Google Scholar
  8. 8.
    D. Kar, D. Cartwright-Smith, Illicit financial flows from developing countries, Global Financial Integrity, A Program of the Center for International Policy, 2002–2006, pp. 1–67Google Scholar
  9. 9.
    S. Mathew, M.S. Sunitha, Types of arcs in a fuzzy graph. Inf. Sci. 179, 1760–1768 (2009)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    S. Mathew, J.N. Mordeson, Connectivity concepts in fuzzy incidence graphs. Inf. Sci. 382–383, 326–333 (2017)MathSciNetCrossRefGoogle Scholar
  11. 11.
    S. Mathew, J.N. Mordeson, Fuzzy incidence blocks and their applications in illegal migration problems. New Math. Nat. Comput. 13(3), 245–260 (2017).  https://doi.org/10.1142/S1793005717400099
  12. 12.
    J.N. Mordeson, Fuzzy incidence graphs. Adv. Fuzzy Sets Syst. 22, 121–133 (2016)CrossRefMATHGoogle Scholar
  13. 13.
    J.N. Mordeson, P.S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs, vol. 46 (Physica-Verlag, Heidelberg, 2000)MATHGoogle Scholar
  14. 14.
    J.N. Mordeson, S. Mathew, Fuzzy end nodes in fuzzy incidence graphs. New Math. Nat. Comput. 13, 13–20 (2017)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    S. Mathew, J.N. Mordeson, Fuzzy influence graphs. New Math. Nat. Comput. 13, 311–325 (2017)Google Scholar
  16. 16.
    A. Rosenfeld, Fuzzy graphs, in Fuzzy Sets and Their Applications, ed. by L.A. Zadeh, K.S. Fu, M. Shimura (Academic Press, London, 1975), pp. 77–95Google Scholar
  17. 17.
    C.H. Smith, Tier rankings and the fight against human trafficking, Congress of the United States, Subcommittee on Africa, Global Health, Global Human Rights, and Int’l Organizations, 2013Google Scholar
  18. 18.
    United Nations on Drug and Crime, UN.GIFT United Nations Initiative to Fight Human Trafficking, An Introduction to Human Trafficking: Vulnerability, Impact, and Action, 2008Google Scholar
  19. 19.
    R.D. Villedas, Central American Migrants and “La Besta”: The Route, Dangers, and Government Response, Migration Information Source, 10 Sept 2014Google Scholar
  20. 20.
    R. Walser, J.B. McNeill, J. Zuckerman, The human tragedy of illegal immigration: greater efforts needed to combat smuggling and violence, Backgrounder, Heritage Foundation No. 2568, 22 June 2011, pp. 1–18Google Scholar
  21. 21.
    S. Worrall, An anthropologist unravels the mysteries of Mexican migration, National Geographic, 6 Dec 2015Google Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  • John N. Mordeson
    • 1
  • Sunil Mathew
    • 2
  • Davender S. Malik
    • 1
  1. 1.Department of MathematicsCreighton UniversityOmahaUSA
  2. 2.Department of MathematicsNational Institute of TechnologyCalicutIndia

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