International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/312 2020 2020 Department of Basic Science, Narula Institute of Technology, Agarpara, Kolkata-700109, India. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, India. Avishek Chakraborty Real-human kind issues have distinct sort of ambiguity and among them; one of the critical troubles is solving the shortest path problem. In this contribution, we applied the developed score function and accuracy function of pentagonal neutrosophic number (PNN) into a shortage path selection problem. Further, a time dependent and heuristic cost function related shortest path algorithm is considered here in PNN area and solved it utilizing an influx of dissimilar rational & pioneer thinking. Lastly, estimation of total ideal time of the graph reflects the importance of this noble work.   2020 2020 21 28 10.54216/IJNS.030104 https://www.americaspg.com/articleinfo/21/show/312