International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1432 2020 2020 Research Scholar, Department of Mathematics, Hindustan Institute of Technology and science, Padur, Chennai, India S. Ghousia Begum Department of Mathematics, St.Joseph’s College of Engineering, Chennai, India N. Jose Parvin .. Department of Mathematics, Hindustan Institute of Technology and Science, Chennai, India A. .. Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India D. Nagarajan Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco Broumi Said 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 2023 68 76 10.54216/IJNS.200106 https://www.americaspg.com/articleinfo/21/show/1432