aspg-21-1339-1791475370 20261008160250 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2022 19 2 N. Jose Parvin Praveena St. Joseph’s College of Engineering, Chennai, India S. Ghousia Begum Hindustan Institute of Technology and Science, Chennai, India A. Rajkumar Hindustan Institute of Technology and Science, Chennai, India D. Nagarajan Department of Mathematics, Rajalakshmi Institute of Technology, Chennai, India broumi said 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 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 66 79 1339 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.190206 https://www.americaspg.com/journal/21/article/1339 https://www.americaspg.com/storage/4613.pdf