aspg-21-312-1791472172 20261008150932 American Scientific Publishing Group admin@americaspg.com American Scientific Publishing Group International Journal of Neutrosophic Science IJNS 2692-6148 2690-6805 2020 3 1 Avishek Chakraborty Department of Basic Science, Narula Institute of Technology, Agarpara, Kolkata-700109, India. Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howra 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 21 28 312 https://creativecommons.org/licenses/by/4.0/ 10.54216/IJNS.030104 https://www.americaspg.com/journal/21/article/312 https://www.americaspg.com/storage/6252.pdf