International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1339 2020 2020 St. Joseph’s College of Engineering, Chennai, India N. Jose Parvin .. Hindustan Institute of Technology and Science, Chennai, India S. Ghousia Begum Hindustan Institute of Technology and Science, Chennai, India A. Rajkumar Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India D. Nagarajan Faculty of Science Ben M’Silk, University of Hassan II,Casablanca, Morocco; Regional Center for the Professions of Education and Training (CRMEF),Casablanca-Settat, Morocco Broumi Said This article discusses Nonagonal Neutrosophic number and m-valued Nonagonal Neutrosophic number. The score function, the accuracy function, hamming distance, normalized hamming distance, Euclidean distance and normalized Euclidean distance of Nonagonal and m-polar Nonagonal Neutrosophic number are derived. Some de-neutrosophication method for Nonagonal Neutrosophic number and some properties of m-valued Nonagonal Neutrosophic number are proved. In this article the optimal path of an acyclic network is estimated using Neutrosophic α-cut  grade, Neutrosophic Euclidean grade technique and dynamic programming recursion method through Nonagonal Neutrosophic number. The score function and the removal area method are used to transform the Nonagonal Neutrosophic number to crisp number and the results obtained in both the methods are compared. 2022 2022 66 79 10.54216/IJNS.190206 https://www.americaspg.com/articleinfo/21/show/1339