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International Journal of Neutrosophic Science

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International Journal of Neutrosophic Science

Volume 19 , Issue 2 , PP: 87-94, 2022 | Cite this article as | XML | Html | PDF | Full Length Article

Different Types of Operations on Neutrosophic Graphs

Arindam Dey 1 * , Ranjan Kumar 2 , Said Broumi 3 , Pritam Bhowmik 4

  • 1 School of Computer Science and Engineering (SCOPE), VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India - (arindam84nit@gmail.com)
  • 2 Department of Mathematics, VIT-AP University, Inavolu, Beside AP Secretariat, Amaravati AP, India - (ranjank.nit52@gmail.com)
  • 3 Faculty of Science Ben M’Sik, University Hassan II, Casablanca, Morocco;Regional Center for the Professions of Education and Training (CRMEF),Casablanca-Settat, Morocco - (broumisaid78@gmail.com)
  • 4 School of Electrical Engineering, Vellore Institute of Technology, Chennai, India - (pritambhowmikjan@gmail.com)

    • Doi: https://doi.org/10.54216/IJNS.190208

    Received: March 19, 2022 Accepted: September 05, 2022
    Abstract

    The fuzzy graph theory uses a substantial and important role in modelling and structuring many optimization

    problems. DIfferent type of uncertainties exist in most of the optimization problems in real lIfe scenarios

    due to indeterminate and incomplete information and it is a challenging task for the expert to design those

    optimization problems applying fuzzy graph. To design the incomplete, uncertainty and vagueness in graphical

    optimization problems, several extensions of graph theoretical ideas are proposed. The idea of neutrosophic

    graph plays an important role to manage the uncertainty, linked with the indeterminate and incomplete

    data/information of any optimization problem. In this manuscript, we present the idea of regular neutrosophic

    graph, strong neutrosophic graph, bipartite neutrosophic graph, regular neutrosophic graph, and regular strong

    neutrosophic graph. We also introduce six different operations on neutrosophic graph, viz., cartesian product,

    composition, join, direct product, lexicographic and strong product.

    Keywords :

    Neutrosophic , uncertainty , neutrosophic graph , bipartite neutrosophic graph.

    References

    [1] L. A. Zadeh, “Fuzzy sets,” Information and control, vol. 8, no. 3, pp. 338–353, 1965.

    [2] F. Smarandache, A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic

    Probability: Neutrsophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability. Infinite

    Study, 2005.

    [3] G. Ghorai and M. Pal, “Certain types of product bipolar fuzzy graphs,” International Journal of Applied

    and Computational Mathematics, vol. 3, no. 2, pp. 605–619, 2017.

    [4] H.-L. Yang, Z.-L. Guo, Y. She, and X. Liao, “On single valued neutrosophic relations,” Journal of Intelligent

    & Fuzzy Systems, vol. 30, no. 2, pp. 1045–1056, 2016.

    [5] J. Ye, “Single-valued neutrosophic minimum spanning tree and its clustering method,” Journal of intelligent

    Systems, vol. 23, no. 3, pp. 311–324, 2014.

    [6] R. A. Borzooei, H. Rashmanlou, S. Samanta, and M. Pal, “Regularity of vague graphs,” Journal of

    Intelligent & Fuzzy Systems, vol. 30, no. 6, pp. 3681–3689, 2016.

    [7] S. Naz, H. Rashmanlou, and M. A. Malik, “Operations on single valued neutrosophic graphs with application,”

    Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2137–2151, 2017.

    Cite This Article As :
    Dey, Arindam. , Kumar, Ranjan. , Broumi, Said. , Bhowmik, Pritam. Different Types of Operations on Neutrosophic Graphs. International Journal of Neutrosophic Science, vol. , no. , 2022, pp. 87-94. DOI: https://doi.org/10.54216/IJNS.190208
    Dey, A. Kumar, R. Broumi, S. Bhowmik, P. (2022). Different Types of Operations on Neutrosophic Graphs. International Journal of Neutrosophic Science, (), 87-94. DOI: https://doi.org/10.54216/IJNS.190208
    Dey, Arindam. Kumar, Ranjan. Broumi, Said. Bhowmik, Pritam. Different Types of Operations on Neutrosophic Graphs. International Journal of Neutrosophic Science , no. (2022): 87-94. DOI: https://doi.org/10.54216/IJNS.190208
    Dey, A. , Kumar, R. , Broumi, S. , Bhowmik, P. (2022) . Different Types of Operations on Neutrosophic Graphs. International Journal of Neutrosophic Science , () , 87-94 . DOI: https://doi.org/10.54216/IJNS.190208
    Dey A. , Kumar R. , Broumi S. , Bhowmik P. [2022]. Different Types of Operations on Neutrosophic Graphs. International Journal of Neutrosophic Science. (): 87-94. DOI: https://doi.org/10.54216/IJNS.190208
    Dey, A. Kumar, R. Broumi, S. Bhowmik, P. "Different Types of Operations on Neutrosophic Graphs," International Journal of Neutrosophic Science, vol. , no. , pp. 87-94, 2022. DOI: https://doi.org/10.54216/IJNS.190208

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