International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/3767 2020 2020 Department of Mathematics, Loyola College, Chennai - 600034, Tamil Nadu, India E. E. Department of Science and Humanities, RMK College of Engineering and Technology, Chennai – 601206, Tamil Nadu, India R. C. Thivyarathi Department of Science and Humanities, Nehru Institute of Engineering and Technology, Coimbatore, Tamil Nadu - 641105, India E. Kungumaraj Department of Information Technology, Panimalar Engineering College, Varadharajapuram, Poonamallee, Chennai-600123, Tamil Nadu, India K. Sridharan Department of Mathematics, Velammal College of Engineering and Technology, Madurai-625009, Tamil Nadu, India V. Dhanasekaran Department of Mathematics, Vel Tech Rangarajan Dr. Sagunthala R& D Institute of Science and Technology, Avadi, Chennai – 600062, Tamil Nadu, India K. A. Venkatesan Pentagonal Neutrosophic Set is a powerful technique for modelling situation in real life where there is uncertainty, indeterminacy, and inconsistency, the PNTP is an advanced version of classical transportation problems. Traditional transportation models do not perform well with imprecise data unlike PNTP that offers a powerful framework that can handle truth, indeterminacy, falsity, non-membership, and membership parameters resulting in a more realistic decision about logistics. In this work, we present a novel Topologized Graphical Method (TGM) for resolving the PNTP, which uses graphical notations to visualize and analyse intricate interactions in transport networks under neutrosophic circumstances. In this paper, an efficient and structured solution methodology has been developed for optimization of PNTP, with TGM incorporated to provide a systematic approach to the PNTP while significantly reducing computational burden. To improve the pragmatism of the method, an algorithm is established in Python to convert the neutrosophic transportation model into a classical transportation problem, which contributes to computing efficiency and helps the decision-makers get the optimal solutions with little efforts. Solutions to numerical examples and case studies, which show that our method achieves better performance than conventional approach in minimizing transportation cost, optimizing resources allocation, and reducing the burden of calculation, provide validation of the proposed method. This research employs Pentagonal Neutrosophic Sets with the TGM as well as the use of the Python programming language to offer an effective and accurate decision-support instrument, improving transportation planning in uncertain dynamic environments. In addition, the findings provide tangible insights into how PNTP could be beneficial in real-world applications, particularly in fields like logistics, SCM, and network design, where managing uncertain information is essential. The next step of this work will be analysing the integration of AI and ML techniques with the presented method to gain improvements on predictive analytics, automation, and real-time decision-making abilities in transportation problems. 2025 2025 143 157 10.54216/IJNS.260310 https://www.americaspg.com/articleinfo/21/show/3767