aspg-21-1432-1791472390 20261008151310 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2023 20 1 S. Ghousia Begum Research Scholar, Department of Mathematics, Hindustan Institute of Technology and science, Padur, Chennai, India N. Jose Parvin Praveena Department of Mathematics, St.Joseph’s College of Engineering, Chennai, India A. Rajkumar Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, India D. Nagarajan Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India broumi said Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco The following paper introduces a methodology to calculate the least cost for a directed network through Travelling salesman problem. Dynamic programming method is used to find the minimum Cost. The recursion formula is used. The edge weights of the networks are being taken in terms of Triangular, Trapezoidal and Pentagonal Neutrosophic set. Score function for the Triangular, Trapezoidal and Pentagonal Neutrosophic sets are being defined for deneutrosophication. The least cost is estimated using all the above said Neutrosophic sets and the result is compared 2023 68 76 1432 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.200106 https://www.americaspg.com/journal/21/article/1432 https://www.americaspg.com/storage/11672828104.pdf