1 Affiliation : Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur – 635 601, Tirupattur District, Tamil Nadu, INDIA
Email : email@example.com
2 Affiliation : Department of Mathematics, Sacred Heart College (Autonomous), Tirupattur – 635 601, Tirupattur District, Tamil Nadu, INDIA
Email : firstname.lastname@example.org
In this paper, we present the new idea of pythagorean neutrosophic fuzzy graphs (PNFG). Pythagorean neutrosophic set [PNS] is a generalization of neutrosophic set with dependent neutrosophic components and Pythagorean fuzzy set with condition 0≤〖μ_A (x)〗^2+〖β_A (x)〗^2+〖σ_A (x)〗^2≤2 . The main aim of this article is to apply pythagorean neutrosophic set to fuzzy graphs. Thus we extend some of the basic properties for this PNFG along with few examples.
Pythagorean neutrosophic set , Pythagorean neutrosophic graphs , Neutrosophic set.
 Zadeh, L.A., “Fuzzy Sets”, Inform. and Control, Vol 8, pp.338- 353, 1965.
 Atanassov, K., “Intuitionistic Fuzzy Sets”, Fuzzy Sets and Systems, Vol 20, pp.87-96, 1986.
 Yager, R.R., “Pythagorean Fuzzy Subsets”, In:Proc Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp.57-61, 2013.
 Smarandache, F., “A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability”, American Research Press: Rehoboth, DE, USA, pp.1-141, 1999.
 Jansi, R., Mohana, R.K., & Smarandache, F., “Correlation Measure for Pythagorean Neutrosophic Fuzzy Sets with T and F as Dependent Neutrosophic Components”, Neutrosophic Sets and Systems, Vol 30(1), pp.202-212, 2019.
 Ajay, D., Charisma, J. J., & Chellamani, P., “Fuzzy Magic and Bi-magic Labelling of Intuitionistic Path Graph”, International Journal of Recent Technology and Engineering, Vol 8(4), pp.11508-11512, 2019.
 Ajay, D., & Chellamani, P., “Fuzzy Magic Labelling of Neutrosophic Path and Star graph”, Advances in Mathematics: Scientific Journal Vol 9(8), pp.6059-6070, 2020.
 Hussain, S.S., Hussain, R.J., Jun, Y.B., & Smarandache, F., “Neutrosophic bipolar vague set and its application to neutrosophic bipolar vague graphs”, Neutrosophic Sets and Systems, Vol 28, pp.69-86, 2019.
 Hussain, S.S., Hussain, R.J., & Muhiuddin, G., “Neutrosophic Vague Line Graphs”, Neutrosophic Sets and Systems, Vol 36, pp.121-130. 2020.
 Hussain, S.S., Hussain, R.J., & Smarandache, F., “On neutrosophic vague graphs”, Neutrosophic Sets and Systems, Vol 28, pp.245-258, 2019.
 Dhavaseelan, R., Jafari, S., Farahani, M.R., & Broumi, S., “On single-valued co-neutrosophic graphs”, Neutrosophic Sets and Systems: An International Book Series in Information Science and Engineering, vol. 22/2018, 22. 2018.
 Akram, M., Khan, A., & Borumand Saeid, A., “Complex Pythagorean Dombi fuzzy operators using aggregation operators and their decision‐making”, Expert Systems, pp.1-28, 2020.
 Ajay, D., Broumi, S., & Aldring, J., “An MCDM Method under Neutrosophic Cubic Fuzzy Sets with Geometric Bonferroni Mean Operator”, Neutrosophic Sets and Systems, Vol 32(1), pp.187-202, 2020.
 Ajay, D., Manivel, M., & Aldring, J., “Neutrosophic Fuzzy SAW Method and It’s Application”, Vol 11, pp.881-887, 2019.
 Ajay, D., Aldring, J., Abirami, S., & Jeni Seles Martina, D., “A SVTrN-number approach of muliti-objective optimization on the basis of simple ration analysis based on MCMD method”, International Journal of Neutrosophic Science, Vol 5(1), 16-28, 2020.
 Ajay, D., & Aldring, J., “A Decision Making Technique Based on Similarity Measure and Entropy of Bipolar Neutrosophic Sets”, The International journal of analytical and experimental modal analysis, Vol 11(9), pp.520-529, 2019.
 Mullai, M., Broumi, S., & Jeyabalan, R., “Homomorphism and Isomorphism in strong neutrosophic graphs”, International Journal of Neutrosophic Science, Vol 0, pp.08-20, 2020.
 Mullai, M., & Broumi, S., “Dominating energy in neutrosophic graphs”, International Journal of Neutrosophic Science, Vol 5(1), pp.38-58, 2020.