International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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2690-6805ISSN (Online) 2692-6148ISSN (Print)

Volume 26 , Issue 3 , PP: 273-278, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Some Results on Neutrosophic Graphs in Neutrosophic Topological space

Gazwan Haider Abdulhusein 1 * , Dalia Raad Abd 2 , Wadei Faris Al-omeri 3

  • 1 Department of Mathematics, Open Educational College, Ministry of Education, Baghdad, Iraq - (g.h.abdulhusein@gmail.com)
  • 2 Department of Mathematics, College of Education, Al-Mustansiriyah University, Baghdad, Iraq - (daliaraad864@uomustansiriyah.edu.iq)
  • 3 Department of Mathematics, Faculty of Science, Jadara University, Irbid, Jordan - (wadeimoon1@hotmail.com)
  • Doi: https://doi.org/10.54216/IJNS.260319

    Received: January 14, 2025 Revised: February 13, 2025 Accepted: March 10, 2025
    Abstract

    A tools and techniques of neutrosophic graph have found many applications in different areas such as topology, networks, computer of science, etc. In addition, neutrosophic graph is a generalization of intuitionistic fuzzy graph. Therefore, in this paper we study some characteristics of neutrosopheic graphs (NTCG) and some basic definitions. Moreover we investigate several kinds of arcs,  -strong, -strong,  -arc, and  -strong, -strong,  –arc in neutrosopheic graphs (NTCG) , Finally we give neutrosophic -bridge and neutrosophic -bridge (NTC -bridge) and some interesting properties of  neutrosophic bridge (NTCB), which is being taught for the first time, and obtain several important properties.

    Keywords :

    Neutrosopheic set , &eta , _&mu , -strong , &sigma , _&mu , -strong , &mu , -bridge , &xi , -bridge , &mu , _*-tree , Ϣ_*-tree , &xi , -tree

    References

    [1]       A. Rosenfeld, "Fuzzy graphs," in L.A. Zadeh, K.S. Fu, and M. Shimura, Eds., Fuzzy Sets and their Applications to Cognitive and Decision Processes, Academic Press, New York, 1975, pp. 77-95.

    [2]       A. Salama and S. Al-Blowi, "Generalized neutrosophic set and generalized neutrosophic topological spaces," Computer Science and Engineering, vol. 2, no. 7, pp. 129-132, 2012.

    [3]       S. Broumi, M. Talea, F. Smarandache, and A. Bakali, "Single valued neutrosophic graphs: degree, order and size," in 2016 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 2444-2451.

    [4]       C.L. Chang, "Fuzzy topological spaces," J. Math. Anal. Appl., vol. 24, pp. 182-190, 1968.

    [5]       F. G. Lupianez, "On neutrosophic topology," International Journal of Systems and Cybernetics, vol. 37, no. 6, pp. 797-800, 2008.

    [6]       F. G. Lupianez, "Interval neutrosophic sets and topology," International Journal of Systems and Cybernetics, vol. 38, no. 3/4, pp. 621-624, 2009.

    [7]       F. Smarandache, "Neutrosophic set: a generalization of the intuitionistic fuzzy set," International Journal of Pure and Applied Mathematics, vol. 24, no. 3, pp. 287-297, 2005.

    [8]       F. Smarandache, "An Introduction to Neutrosophy and Neutrosophic Logic, Neutrosophic set, and Neutrosophic Probability and Statistics," in First International Conference, University of New Mexico, Gallup, NM, USA, 2002.

    [9]       K. Atanassov, "Intuitionistic fuzzy sets," Fuzzy Sets and Systems, vol. 20, pp. 87-96, 1986.

    [10]    K. Atanassov, "Review and new result on intuitionistic fuzzy sets," preprint IM-MFAIS-1-88, So_a, 1988.

    [11]    L.A. Zadeh, "Fuzzy sets," Inform. Control, vol. 8, pp. 338-353, 1965.

    [12]    P. Bhattacharya, "Some remarks on fuzzy graphs," Pattern Recognition Letters, vol. 6, pp. 297-302, 1987.

    [13]    R.T. Yeh and S. Y. Bang, "Fuzzy relations, fuzzy graphs and their applications to clustering analysis," in L.A. Zadeh, K.S. Fu, and M. Shimura, Eds., Fuzzy Sets and their Applications to Cognitive and Decision Processes, Academic Press, New York, 1975, pp. 125-149.

    [14]    J. K. Patel and A. R. Kumar, "Applications of neutrosophic logic in decision-making under uncertainty," Journal of Computational Science, vol. 45, pp. 101234, 2023.

    [15]    W. Al-Omeri and M. Kaviyarasu, "Study on neutrosophic graph with application on earthquake response center in Japan," Symmetry, vol. 16, no. 6, pp. 743, 2024.

    [16]    M. T. Garcia and N. H. Lee, "A novel approach to cybersecurity using neutrosophic sets," International Journal of Information Security, vol. 18, no. 2, pp. 123-135, 2022.

    [17]   W. Al-Omeri, "On fuzzy completely irresolute on smart decision-making for electric vehicle systems," in Artificial Intelligence-Empowered Modern Electric Vehicles in Smart Grid Systems, Elsevier, 2024, pp. 397-416.

    Cite This Article As :
    Haider, Gazwan. , Raad, Dalia. , Faris, Wadei. Some Results on Neutrosophic Graphs in Neutrosophic Topological space. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 273-278. DOI: https://doi.org/10.54216/IJNS.260319
    Haider, G. Raad, D. Faris, W. (2025). Some Results on Neutrosophic Graphs in Neutrosophic Topological space. International Journal of Neutrosophic Science, (), 273-278. DOI: https://doi.org/10.54216/IJNS.260319
    Haider, Gazwan. Raad, Dalia. Faris, Wadei. Some Results on Neutrosophic Graphs in Neutrosophic Topological space. International Journal of Neutrosophic Science , no. (2025): 273-278. DOI: https://doi.org/10.54216/IJNS.260319
    Haider, G. , Raad, D. , Faris, W. (2025) . Some Results on Neutrosophic Graphs in Neutrosophic Topological space. International Journal of Neutrosophic Science , () , 273-278 . DOI: https://doi.org/10.54216/IJNS.260319
    Haider G. , Raad D. , Faris W. [2025]. Some Results on Neutrosophic Graphs in Neutrosophic Topological space. International Journal of Neutrosophic Science. (): 273-278. DOI: https://doi.org/10.54216/IJNS.260319
    Haider, G. Raad, D. Faris, W. "Some Results on Neutrosophic Graphs in Neutrosophic Topological space," International Journal of Neutrosophic Science, vol. , no. , pp. 273-278, 2025. DOI: https://doi.org/10.54216/IJNS.260319