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Generalized Fuzzy Graph Connectivity Parameters with Application to Human Trafficking

Author

Listed:
  • Arya Sebastian

    (Department of Mathematics, National Institute of Technology Calicut, Kerala 673601, India)

  • John N Mordeson

    (Department of Mathematics, Creighton University, Omaha, NE 68178, USA)

  • Sunil Mathew

    (Department of Mathematics, National Institute of Technology Calicut, Kerala 673601, India)

Abstract

Graph models are fundamental in network theory . But normalization of weights are necessary to deal with large size networks like internet. Most of the research works available in the literature have been restricted to an algorithmic perspective alone. Not much have been studied theoretically on connectivity of normalized networks. Fuzzy graph theory answers to most of the problems in this area. Although the concept of connectivity in fuzzy graphs has been widely studied, one cannot find proper generalizations of connectivity parameters of unweighted graphs. Generalizations for some of the existing vertex and edge connectivity parameters in graphs are attempted in this article. New parameters are compared with the old ones and generalized values are calculated for some of the major classes like cycles and trees in fuzzy graphs. The existence of super fuzzy graphs with higher connectivity values are established for both old and new parameters. The new edge connectivity values for some wider classes of fuzzy graphs are also obtained. The generalizations bring substantial improvements in fuzzy graph clustering techniques and allow a smooth theoretical alignment. Apart from these, a new class of fuzzy graphs called generalized t-connected fuzzy graphs are studied. An algorithm for clustering the vertices of a fuzzy graph and an application related to human trafficking are also proposed.

Suggested Citation

  • Arya Sebastian & John N Mordeson & Sunil Mathew, 2020. "Generalized Fuzzy Graph Connectivity Parameters with Application to Human Trafficking," Mathematics, MDPI, vol. 8(3), pages 1-21, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:424-:d:332928
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    References listed on IDEAS

    as
    1. John N. Mordeson & Sunil Mathew, 2017. "Non-Deterministic Flow in Fuzzy Networks and Its Application in Identification of Human Trafficking Chains," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 13(03), pages 231-243, November.
    2. Sunil Mathew & Hai Long Yang & Jill K. Mathew, 2018. "Saturation in Fuzzy Graphs," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 113-128, March.
    3. Shanookha Ali & Sunil Mathew & John N. Mordeson & Hossein Rashmanlou, 2018. "Vertex Connectivity of Fuzzy Graphs with Applications to Human Trafficking," New Mathematics and Natural Computation (NMNC), World Scientific Publishing Co. Pte. Ltd., vol. 14(03), pages 457-485, November.
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    Cited by:

    1. Jayanta Bera & Kinkar Chandra Das & Sovan Samanta & Jeong-Gon Lee, 2023. "Connectivity Status of Intuitionistic Fuzzy Graph and Its Application to Merging of Banks," Mathematics, MDPI, vol. 11(8), pages 1-25, April.
    2. Azadeh Zahedi Khameneh & Adem Kilicman & Fadzilah Md Ali, 2021. "Revision of Pseudo-Ultrametric Spaces Based on m-Polar T-Equivalences and Its Application in Decision Making," Mathematics, MDPI, vol. 9(11), pages 1-18, May.

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