| Title of paper:
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Properties of fuzzy chromatic numbers in intuitionistic fuzzy graphs
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| Author(s):
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R. Buvaneswari 0009-0009-0822-6761
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| Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore - 8, Tamil Nadu, India
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| buvanaamohan@gmail.com
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P. Revathy 0000-0001-8531-4700
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Department of Mathematics, Sri Krishna Arts and Science College, Coimbatore - 8, Tamil Nadu, India Department of Mathematics, Sri Krishna College of Engineering and Technology, Coimbatore - 8, Tamil Nadu, India
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| revaprabhu92@gmail.com
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| Published in:
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Notes on Intuitionistic Fuzzy Sets, Volume 31 (2025), Number 3, pages 346–357
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| DOI:
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https://doi.org/10.7546/nifs.2025.31.3.346-357
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| Download:
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PDF (350 Kb, File info)
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| Abstract:
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The theory of fuzzy coloring is analyzed with its properties in consideration of the Intuitionistic Fuzzy Graphs (IFGs) nature. The fuzzy chromatic number obtained by applying fuzzy coloring technique to the vertices and edges of IFGs are examined.
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| Keywords:
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Fuzzy coloring, Strong fuzzy colors, Fuzzy chromatic number, Intuitionistic fuzzy graphs.
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| AMS Classification:
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05C15, 05C72.
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| References:
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- Atanassov, K. T. (1983). Intuitionistic fuzzy sets. VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: International Journal Bioautomation, 2016, 20(S1), S1–S6.
- Atanassov, K. T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87–96.
- Atanassov, K. T. (1999). Intuitionistic Fuzzy Sets: Theory and Applications. Springer Physica-Verlag, Heidelberg.
- Behzad, M. (1965). Graphs and Their Chromatic Numbers. Ph.D Thesis, Michigan State University, East Lansing.
- Buvaneswari, R., & Revathy, P. (2023). Fuzzy coloring and total fuzzy coloring of various types of intuitionistic fuzzy graphs. Notes on Intuitionistic Fuzzy Sets, 29(4), 383–400.
- Buvaneswari, R., & Revathy, P. (2025). An application of a strong and complete intuitionistic fuzzy graph by the concept of fuzzy coloring. Notes on Intuitionistic Fuzzy Sets, 31(1), 39–47.
- Chartrand, G., & Zhang, P. (2009). Chromatic Graph Theory. CRC Press, A Chapman and Hall Book.
- Eslahchi, C., & Onagh, B. N. (2006). Vertex-strength of fuzzy graphs. International Journal of Mathematics and Mathematical Sciences, 1, 1–9.
- Jahir Hussain, R., & Kanzul Fathima, K. S. (2016). An introduction to fuzzy edge coloring. Journal of Advances in Mathematics, 11(10), 5742–5748.
- Karunambigai, M. G., Parvathi, R., & Buvaneswari, R. (2011). Constant intuitionistic fuzzy graphs. Notes on Intuitionistic Fuzzy Sets, 17(1), 37–47.
- Karunambigai, M. G., Parvathi, R., & Buvaneswari, R. (2012). Arcs in intuitionistic fuzzy graphs. Notes on Intuitionistic Fuzzy Sets, 18(4), 48–58.
- Karunambigai, M. G., Akram, M., & Buvaneswari, R. (2016). Strong and superstrong vertices in intuitionistic fuzzy graphs. Journal of Intelligent and Fuzzy Systems, 30, 671–678.
- Lavanya, S., & Sattanathan, R. (2009). Fuzzy total coloring of fuzzy graphs. International Journal of Information Technology and Knowledge Management, 2(1), 37–39.
- Mahapatra, R., Samanta, S., & Pal, M. (2020). Applications of edge coloring of fuzzy graphs. Informatica, 31(2), 313–330.
- Nivethana, V., & Parvathi, A. (2013). Fuzzy total coloring and chromatic number of a complete fuzzy graph. International Journal of Emerging Trends in Engineering and Development, 6(3), 377–384.
- Parvathi, R., & Karunambigai, M. G. (2006). Intuitionistic fuzzy graphs. In: Reusch, B. (Ed.). Computational Intelligence, Theory and Applications, Vol 38., 139–150. Springer, Berlin, Heidelberg.
- Prasanna, A., Rifayathali, M. A., & Ismail Mohideen, S. (2017). Strong intuitionistic fuzzy graph coloring. International Journal of Latest Engineering Research and Applications (IJLERA), 2(8), 163–169.
- Rifayathali, M. A., Prasanna, A., & Ismail Mohideen, S. (2018). Intuitionistic fuzzy graph coloring. International Journal of Research and Analytical Reviews, 5(3), 734–742.
- Rosenfeld, A. (1975). Fuzzy graphs. Academic Press, 77–95.
- Samanta, S., Pramanik, T., & Pal, M. (2015). Fuzzy coloring of fuzzy graphs. Afrika Matematika, 27, 37–50.
- Shannon, A., & Atanassov, K. T. (1994). A first step to a theory of the intuitionistic fuzzy graphs. Proceedings of the First Workshop on Fuzzy Based Expert Systems (D. Lakov, Ed.), Sofia, 28–30 September 1994, 59–61.
- Vizing, V. G. (1963). The Cartesian product of graphs. Vychislitel’nye Sistemy, 9, 30–43.
- Yahya Mohamed, S., & Mohamed Ali, A., (2021). Complement of max product of intuitionistic fuzzy graphs. Complex & Intelligent systems, 7, 2895–2905.
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