Picture fuzzy labelling graphs with an application

Document Type : Original Article


1 Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur, Tamilnadu

2 Ph. D Research Scholar, PG and Research Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur – 635 601, Tamil Nadu


The main objective of this paper is to introduce the idea of picture fuzzy labelling of graphs and the concepts of strong arc, partial cut node, bridge of picture fuzzy labelling graphs, picture fuzzy labelling tree and cycle along with their properties and results. In addition, an application of the picture fuzzy graph labelling model for the human circulatory system has been discussed.


Ajay, D., & Aldring, J. (2019). A Decision Making Technique Based on Similarity Measure and Entropy of Bipolar Neutrosophic Sets. The International journal of analytical and experimental modal analysis, 11(9), 520-529.‏
Ajay, D., Aldring, J., Seles Martina, D. J., & Abirami, S. A. (2020). A SVTrN-number approach of multi-objective optimisation on the basis of simple ratio analysis based on MCDM method. International Journal of Neutrosophic Science, 5(1), 16-28.‏
Ajay, D., and Chellamani, P. (2020). Fuzzy magic labelling of Neutrosophic path and star graph, Advances in Mathematics: Scientific Journal, 9(8), p.6059–6070.
Ajay, D., Broumi, S., & Aldring, J. (2020). An MCDM method under neutrosophic cubic fuzzy sets with geometric bonferroni mean operator. Neutrosophic Sets and Systems, 32, 187-202.‏
Ajay, D., Charisma, J. J., & Chellamani, P. (2019). Fuzzy Magic and Bi-magic Labelling of Intuitionistic Path Graph. International Journal of Recent Technology and Engineering, 8(4), 11508-11512.‏
Ajay, D., Manivel, M., & Aldring, J. (2019). Neutrosophic Fuzzy SAW Method and It’s Application. The International journal of analytical and experimental modal analysis, 11, 881-887.‏
Atanassov, K.T. (1986); Intuitionstic fuzzy sets, Fuzzy sets and systemsVol. 20(1), pp.87-96.
Cường, B. C. (2014). Picture fuzzy sets. Journal of Computer Science and Cybernetics, 30(4), 409.‏
Cuong, B. C., & Kreinovich, V. (2013, December). Picture Fuzzy Sets-a new concept for computational intelligence problems. In 2013 third world congress on information and communication technologies (WICT 2013) (pp. 1-6). IEEE.‏
Cuong, B. C., Huyen, P. T., Van Chien, P., & Van Hai, P. (2019, October). Some Fuzzy Inference Processes in Picture Fuzzy Systems. In 2019 11th International Conference on Knowledge and Systems Engineering (KSE) (pp. 1-5). IEEE.‏
Deli, I., & Öztürk, E. K. (2020). Two Centroid Point for SVTN-Numbers and SVTrN-Numbers: SVN-MADM Method. In Neutrosophic Graph Theory and Algorithms (pp. 279-307). IGI Global.‏
Deli, I., & Şubaş, Y. (2017). Some weighted geometric operators with SVTrN-numbers and their application to multi-criteria decision making problems. Journal of Intelligent & Fuzzy Systems, 32(1), 291-301.‏
Kaufmann, A. (1975). Theory of fuzzy subsets: introduction to the. Fundamental theoretical elements. Academic Press.‏
Nagoor Gani, A., & Akram, M. (2014). Novel properties of fuzzy labeling graphs. Journal of Mathematics, 2014.‏
Rosa, A. (1966, July). Theory of graphs. In International Symposium, Rome, July (pp. 349-355).‏
Rosenfeld, A. (1975). Fuzzy graphs. In Fuzzy sets and their applications to cognitive and decision processes (pp. 77-95). Academic press.‏
Smarandache, F., A (1999).Unifying Field in Logics, Neutrosophic Logic: Neutrosophy, Neutrosophic Set, Neutrosophic Probability, Rehoboth: American Research Press.
 Zadeh, L.A., (1965) Fuzzy sets, Information and Control.; Vol. 8, pp. 338-353.
Zuo, C., Pal, A., & Dey, A. (2019). New concepts of picture fuzzy graphs with application. Mathematics, 7(5), 470.‏